Write a 125-word essay on the following topics 1. Why do you think such appalling conditions were allowed to exist in American factories during the Industrial Revolution? 2. How do you propose to be able to do all the things your text says are duties of the safety professional? 3. How Has the Culture of an Organization Positively or Negatively Affected Your Performance? 4. The primary motivation in loss control is financial. Should saving company money be our primary concern? 5. Do You Think Workers’ Compensation is Fair to Employees and Employers? 6. Our book suggests that we fix only hazards which have cost/benefit. Is this immoral? 7. Why should the Supervisor and not the Safety Manager be the primary person to investigate incidents? 8. Do you believe our anti-terrorism efforts in this country will prevent further terrorist attacks? 9. What has been the most effective training you have ever had? Why? 10. What do you believe to be some challenges in Industrial Safety for the future?

Write a 125-word essay on the following topics 1. Why do you think such appalling conditions were allowed to exist in American factories during the Industrial Revolution? 2. How do you propose to be able to do all the things your text says are duties of the safety professional? 3. How Has the Culture of an Organization Positively or Negatively Affected Your Performance? 4. The primary motivation in loss control is financial. Should saving company money be our primary concern? 5. Do You Think Workers’ Compensation is Fair to Employees and Employers? 6. Our book suggests that we fix only hazards which have cost/benefit. Is this immoral? 7. Why should the Supervisor and not the Safety Manager be the primary person to investigate incidents? 8. Do you believe our anti-terrorism efforts in this country will prevent further terrorist attacks? 9. What has been the most effective training you have ever had? Why? 10. What do you believe to be some challenges in Industrial Safety for the future?

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Read the excerpt provided, then answer the questions below. http://www.ourdocuments.gov/doc.php?flash=true&doc=23&page=transcript What is the line of division suggested by the Monroe Doctrine? A. It establishes a dividing line that leaves all of the Americas to the United States. B. It establishes a sphere of security that ends roughly at the divide between Central and South America. C. It states that anything south of the U.S. border is available for colonization but nothing north of it. D. It establishes a division of territorial control between the United States and Canada. E. It establishes a division between East and West Germany. What does the Monroe Doctrine establish in terms of the U.S. realm of security? A. An agreement among South American states to protect themselves against European and U.S. intervention. B. A declaration that establishes South and Central America as included into the U.S. sphere of security and that intervention by Europe would be met with hostility. C. A European policy of non-intervention into the Americas. D. A treaty of mutual cooperation between Europe and the United States to protect each other’s colonies. E. A free trade sphere among North and South America. What does the Monroe Doctrine indicate in terms of European colonization of Central and South America? A. A policy of cooperative assistance, if Europe wishes to colonize South American countries we will assist. B. A policy of non-interference, the colonization of South American countries by European states will be considered a threat to U.S. security interests. C. A policy of the expansion of the rights of Central and South American states. D. The creation of a unified group of colonies including the U.S. and European colonies for collective security. E. A policy of complete cooperation and humanitarian development through aid dollars. For the newly independent states who were at one point European colonies, what does the Doctrine indicate? A. That the United States sees the rights of the European countries to reestablish control of those territories. B. That the United States will take over and colonize those countries rather than allow the Europeans to re-establish control. C. That the United States sees no legitimacy in recognizing the newly independent states who are stable. D. That the United States supports the maintenance of the independence of those former colonies. E. That the United States will accept payment for the loss of control over those former colonies.

Read the excerpt provided, then answer the questions below. http://www.ourdocuments.gov/doc.php?flash=true&doc=23&page=transcript What is the line of division suggested by the Monroe Doctrine? A. It establishes a dividing line that leaves all of the Americas to the United States. B. It establishes a sphere of security that ends roughly at the divide between Central and South America. C. It states that anything south of the U.S. border is available for colonization but nothing north of it. D. It establishes a division of territorial control between the United States and Canada. E. It establishes a division between East and West Germany. What does the Monroe Doctrine establish in terms of the U.S. realm of security? A. An agreement among South American states to protect themselves against European and U.S. intervention. B. A declaration that establishes South and Central America as included into the U.S. sphere of security and that intervention by Europe would be met with hostility. C. A European policy of non-intervention into the Americas. D. A treaty of mutual cooperation between Europe and the United States to protect each other’s colonies. E. A free trade sphere among North and South America. What does the Monroe Doctrine indicate in terms of European colonization of Central and South America? A. A policy of cooperative assistance, if Europe wishes to colonize South American countries we will assist. B. A policy of non-interference, the colonization of South American countries by European states will be considered a threat to U.S. security interests. C. A policy of the expansion of the rights of Central and South American states. D. The creation of a unified group of colonies including the U.S. and European colonies for collective security. E. A policy of complete cooperation and humanitarian development through aid dollars. For the newly independent states who were at one point European colonies, what does the Doctrine indicate? A. That the United States sees the rights of the European countries to reestablish control of those territories. B. That the United States will take over and colonize those countries rather than allow the Europeans to re-establish control. C. That the United States sees no legitimacy in recognizing the newly independent states who are stable. D. That the United States supports the maintenance of the independence of those former colonies. E. That the United States will accept payment for the loss of control over those former colonies.

Read the excerpt provided, then answer the questions below. http://www.ourdocuments.gov/doc.php?flash=true&doc=23&page=transcript … Read More...
6. (20 pts) (Nilsson & Riedel, p. 391, 10.34.) A group of small appliances on a 60Hz system requires 20kVA at 0.85 lagging pf when operated at 125 VRMS. The impedance of the line supplying the appliances is 0.01 +j0.08 Ω. The voltage at the load end of the line is 125VRMS. a) What is the RMS magnitude of the voltage at the Source? b) What is the average power loss in the line, PLINE? c) What size of capacitor in μF across the load end of the feeder is needed to change the load pf to 1. d) After the capacitor is installed, what is VRMS at the source, if the load voltage is maintained at 125VRMS? e) What is the average power loss in the line, PLINE with the capacitor installed?

6. (20 pts) (Nilsson & Riedel, p. 391, 10.34.) A group of small appliances on a 60Hz system requires 20kVA at 0.85 lagging pf when operated at 125 VRMS. The impedance of the line supplying the appliances is 0.01 +j0.08 Ω. The voltage at the load end of the line is 125VRMS. a) What is the RMS magnitude of the voltage at the Source? b) What is the average power loss in the line, PLINE? c) What size of capacitor in μF across the load end of the feeder is needed to change the load pf to 1. d) After the capacitor is installed, what is VRMS at the source, if the load voltage is maintained at 125VRMS? e) What is the average power loss in the line, PLINE with the capacitor installed?

(Nilsson & Riedel, p. 391, 10.34.) A group of small appliances on a 60Hz system requires 20kVA at 0.85 lagging pf when operated at 125 VRMS. The impedance of the line supplying the appliances is 0.01 +j0.08 Ω. The voltage at the load end of the line is 125VRMS. a) What is the RMS magnitude of the voltage at the Source? b) What is the average power loss in the line, PLINE? c) What size of capacitor in μF across the load end of the feeder is needed to change the load pf to 1. d) After the capacitor is installed, what is VRMS at the source, if the load voltage is maintained at 125VRMS? e) What is the average power loss in the line, PLINE with the capacitor installed

(Nilsson & Riedel, p. 391, 10.34.) A group of small appliances on a 60Hz system requires 20kVA at 0.85 lagging pf when operated at 125 VRMS. The impedance of the line supplying the appliances is 0.01 +j0.08 Ω. The voltage at the load end of the line is 125VRMS. a) What is the RMS magnitude of the voltage at the Source? b) What is the average power loss in the line, PLINE? c) What size of capacitor in μF across the load end of the feeder is needed to change the load pf to 1. d) After the capacitor is installed, what is VRMS at the source, if the load voltage is maintained at 125VRMS? e) What is the average power loss in the line, PLINE with the capacitor installed

One of the primary health risks of sexual activity in women include Question 3 options: weight loss unwanted pregnancy weight gain a tendency toward bisexuality

One of the primary health risks of sexual activity in women include Question 3 options: weight loss unwanted pregnancy weight gain a tendency toward bisexuality

One of the primary health risks of sexual activity in … Read More...
Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11<Z<0.22) (f) P(-0.11<Z<0.5) Q.19. Use normal distribution table to find the missing values (?). (a) P(Z< ?)=0.40 (b) P(Z< ?)=0.76 (c) P(Z> ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11 ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

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1 MECE2320U-THERMODYNAMICS HOMEWORK # 5 Instructor: Dr. Ibrahim Dincer Assignment Date: Thursday, 22 October 2015 Assignment Type: Individual Due Date: Thursday, 29 October 2015 (3.00 pm latest, leave in dropbox 8) 1) As shown in figure, the inlet and outlet conditions of a steam turbine are given. The heat loss from turbine is 35 kJ per kg of steam. a) Show all the state points on T-v diagram b) Write mass and energy balance equations c) Calculate the turbine work 2) As shown in figure, refrigerant R134a enters to a compressor. Write both mass and energy balance equations. Calculate the compressor work and the mass flow rate of refrigerant. 3) As shown in figure, the heat exchanger uses the heat of hot exhaust gases to produce steam. Where, 15% of heat is lost to the surroundings. Exhaust gases enters the heat exchanger at 500°C. Water enters at 15°C as saturated liquid and exit at saturated vapor at 2 MPa. Mass flow rate of water is 0.025 kg/s, and for exhaust gases, it is 0.42 kg/s. The specific heat for exhaust gases is 1.045 kJ/kg K, which can be treated as ideal gas. 1 Turbine 2 ? 1 = 1 ??/? ?1 = 1 ??? ?1 = 300 ℃ ?1 = 40 ?/? ? ??? =? ????? = 35 ??/?? ?2 = 150 ??? ?2 = 0.9 ?2 = 180 ?/? 1 Compressor 2 ???? ???? = 1.3 ?3/??? ?1 = 100 ??? ?1 = −20 ℃ ? ?? =? ? ???? = 3 ?? ?2 = 800 ??? ?2 = 60 ℃ 2 a) Write mass and energy balance equations. b) Calculate the rate of heat transfer to the water. c) Calculate the exhaust gases exit temperature. 4) As shown in figure, two refrigerant R134a streams mix in a mixing chamber. If the mass flow rate of cold stream is twice that of the hot stream. a) Write mass and energy balance equations. b) Calculate the temperature of the mixture at the exit of the mixing chamber c) Calculate the quality at the exit of the mixing chamber 5) As shown in figure, an air conditioning system requires airflow at the main supply duct at a rate of 140 m3/min. The velocity inside circular duct is not to exceed 9 m/s. Assume that the fan converts 85% of electrical energy it consumes into kinetic energy of air. a) Write mass and energy balance equations. b) Calculate the size of electric motor require to drive the fan c) Calculate the diameter of the main duct ?2 = 1 ??? ?2 = 90 ℃ ?1 = 1 ??? ?1 = 30 ℃ ?3 =? ?3 =? 140 ?3/??? 9 ?/? Air Fan

1 MECE2320U-THERMODYNAMICS HOMEWORK # 5 Instructor: Dr. Ibrahim Dincer Assignment Date: Thursday, 22 October 2015 Assignment Type: Individual Due Date: Thursday, 29 October 2015 (3.00 pm latest, leave in dropbox 8) 1) As shown in figure, the inlet and outlet conditions of a steam turbine are given. The heat loss from turbine is 35 kJ per kg of steam. a) Show all the state points on T-v diagram b) Write mass and energy balance equations c) Calculate the turbine work 2) As shown in figure, refrigerant R134a enters to a compressor. Write both mass and energy balance equations. Calculate the compressor work and the mass flow rate of refrigerant. 3) As shown in figure, the heat exchanger uses the heat of hot exhaust gases to produce steam. Where, 15% of heat is lost to the surroundings. Exhaust gases enters the heat exchanger at 500°C. Water enters at 15°C as saturated liquid and exit at saturated vapor at 2 MPa. Mass flow rate of water is 0.025 kg/s, and for exhaust gases, it is 0.42 kg/s. The specific heat for exhaust gases is 1.045 kJ/kg K, which can be treated as ideal gas. 1 Turbine 2 ? 1 = 1 ??/? ?1 = 1 ??? ?1 = 300 ℃ ?1 = 40 ?/? ? ??? =? ????? = 35 ??/?? ?2 = 150 ??? ?2 = 0.9 ?2 = 180 ?/? 1 Compressor 2 ???? ???? = 1.3 ?3/??? ?1 = 100 ??? ?1 = −20 ℃ ? ?? =? ? ???? = 3 ?? ?2 = 800 ??? ?2 = 60 ℃ 2 a) Write mass and energy balance equations. b) Calculate the rate of heat transfer to the water. c) Calculate the exhaust gases exit temperature. 4) As shown in figure, two refrigerant R134a streams mix in a mixing chamber. If the mass flow rate of cold stream is twice that of the hot stream. a) Write mass and energy balance equations. b) Calculate the temperature of the mixture at the exit of the mixing chamber c) Calculate the quality at the exit of the mixing chamber 5) As shown in figure, an air conditioning system requires airflow at the main supply duct at a rate of 140 m3/min. The velocity inside circular duct is not to exceed 9 m/s. Assume that the fan converts 85% of electrical energy it consumes into kinetic energy of air. a) Write mass and energy balance equations. b) Calculate the size of electric motor require to drive the fan c) Calculate the diameter of the main duct ?2 = 1 ??? ?2 = 90 ℃ ?1 = 1 ??? ?1 = 30 ℃ ?3 =? ?3 =? 140 ?3/??? 9 ?/? Air Fan

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Vulnerability of [NAME OF PLANT] At-Risk Score: [NUMBER] Described by [Your Name] Scored by [Name of past student] Background Write here about the how the plants is (and has been used) and anything else generally interesting about it. Use parenthetical (Author, Year) notation following Pechenik to note sources of information. End the background section with the score of the plant and a subtle (or not so subtle) transition to why the plant scored as it did, as broken down by subscore, emphasizing which sub-score makes it most vulnerable. Life History Score [Life History Subscore] Explain, in words, why the plant has the score it does for life history. Document following Pechenik. Effects of Harvest on Individuals [Subscore] Explain, in words, why the plant has the score it does for Effects of Harvest on Individuals. Document following Pechenik. Population Size [Subscore] Explain, in words, why the plant has the score it does for population size. Document following Pechenik. Include referenced figures (e.g. range maps) if they illustrate the point. Habitat [Subscore] Explain, in words, why the plant has the score it does for habitat. Document following Pechenik. Include referenced figures (e.g. maps of habitat loss) if they illustrate the point. Demand [Subscore] Explain, in words, why the plant has the score it does for demand. Document following Pechenik. Include referenced figures (e.g. graphs of changes in value or demand) if they illustrate the point. Special Considerations Describe any information that did not fit in the above that might make the plant more or less vulnerable. Also include information about conditions that could change that would warrant the plant being reassessed. References [List references alphabetically by first word following Pechenik] SAVE THE DOCUMENT WITH the title [Genus] score description by [your last name] 2017

Vulnerability of [NAME OF PLANT] At-Risk Score: [NUMBER] Described by [Your Name] Scored by [Name of past student] Background Write here about the how the plants is (and has been used) and anything else generally interesting about it. Use parenthetical (Author, Year) notation following Pechenik to note sources of information. End the background section with the score of the plant and a subtle (or not so subtle) transition to why the plant scored as it did, as broken down by subscore, emphasizing which sub-score makes it most vulnerable. Life History Score [Life History Subscore] Explain, in words, why the plant has the score it does for life history. Document following Pechenik. Effects of Harvest on Individuals [Subscore] Explain, in words, why the plant has the score it does for Effects of Harvest on Individuals. Document following Pechenik. Population Size [Subscore] Explain, in words, why the plant has the score it does for population size. Document following Pechenik. Include referenced figures (e.g. range maps) if they illustrate the point. Habitat [Subscore] Explain, in words, why the plant has the score it does for habitat. Document following Pechenik. Include referenced figures (e.g. maps of habitat loss) if they illustrate the point. Demand [Subscore] Explain, in words, why the plant has the score it does for demand. Document following Pechenik. Include referenced figures (e.g. graphs of changes in value or demand) if they illustrate the point. Special Considerations Describe any information that did not fit in the above that might make the plant more or less vulnerable. Also include information about conditions that could change that would warrant the plant being reassessed. References [List references alphabetically by first word following Pechenik] SAVE THE DOCUMENT WITH the title [Genus] score description by [your last name] 2017

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5. Provide a brief discussion with supporting evidence to the following inquiry: With the responsibility of overseeing career development processes, how does management equip employees with skills that impact their performance in an efficient and effective manner?

5. Provide a brief discussion with supporting evidence to the following inquiry: With the responsibility of overseeing career development processes, how does management equip employees with skills that impact their performance in an efficient and effective manner?

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Question 1 In order to properly manage expenses, the company investigates the amount of money spent by its sales office. The below numbers are related to six randomly selected receipts provided by the staff. $147 $124 $93 $158 $164 $171 a) Calculate ̅ , s2 and s for the expense data. b) Assume that the distribution of expenses is approximately normally distributed. Calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all expenses by the sales office. c) If a member of the sales office submits a receipt with the amount of $190, should this expense be considered unusually high? Explain your answer. d) Compute and interpret the z-score for each of the six expenses. Question 2 A survey presents the results of a concept study for the taste of new food. Three hundred consumers between 18 and 49 years old were randomly selected. After sampling the new cuisine, each was asked to rate the quality of food. The rating was made on a scale from 1 to 5, with 5 representing “extremely agree with the quality” and with 1 representing “not at all agree with the new food.” The results obtained are given in Table 1. Estimate the probability that a randomly selected 18- to 49-year-old consumer a) Would give the phrase a rating of 4. b) Would give the phrase a rating of 3 or higher. c) Is in the 18–26 age group; the 27–35 age group; the 36–49 age group. d) Is a male who gives the phrase a rating of 5. e) Is a 36- to 49-year-old who gives the phrase a rating of 2. f) Estimate the probability that a randomly selected 18- to 49-year-old consumer is a 27- to 49-year-old who gives the phrase a rating of 3. g) Estimate the probability that a randomly selected 18- to 49-year-old consumer would 1) give the phrase a rating of 2 or 4 given that the consumer is male; 2) give the phrase a rating of 4 or 5 given that the consumer is female. Based on the results of parts 1 and 2, is the appeal of the phrase among males much different from the appeal of the phrase among females? Explain. h) Give the phrase a rating of 4 or 5, 1) given that the consumer is in the 18–26 age group; 2) given that the consumer is in the 27–35 age group; 3) given that the consumer is in the 36–49 age group. Table 1. Gender Age Group Rating Total Male Female 18-26 27-35 36-49 Extremely Appealing (5) 151 68 83 48 66 37 (4) 91 51 40 36 36 19 (3) 36 21 15 9 12 15 (2) 13 7 6 4 6 3 Not at all appealing(1) 9 3 6 4 3 2 Question 3 Based on the reports provided by the brokers, it is concluded that the annual returns on common stocks are approximately normally distributed with a mean of 17.8 percent and a standard deviation of 29.3 percent. On the other hand, the company reports that the annual returns on tax-free municipal bonds are approximately normally distributed with a mean return of 4.7 percent and a standard deviation of 10.2 percent. Find the probability that a randomly selected a) Common stock will give a positive yearly return. b) Tax-free municipal bond will give a positive yearly return. c) Common stock will give more than a 13 percent return. d) Tax-free municipal bond will give more than a 11.5 percent return. e) Common stock will give a loss of at least 7 percent. f) Tax-free municipal bond will give a loss of at least 10 percent. Question 4 Based on a sample of 176 workers, it is estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. It is also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. We randomly select a sample of 100 workers. a) What is the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days? Assume σ equals 1.3 days. b) What is the probability that the average amount of unpaid time lost during a three-month period for the 100 workers will exceed 1.5 days? Assume σ equals 1.8 days. c) A sample of 100 workers is randomly selected. Suppose the sample mean amount of unpaid time lost during a three-month period actually exceeds 1.5 days. Would it be reasonable to conclude that the mean amount of unpaid time lost has increased above the previously estimated 1.0 day? Explain. Assume σ still equals 1.8 days.

Question 1 In order to properly manage expenses, the company investigates the amount of money spent by its sales office. The below numbers are related to six randomly selected receipts provided by the staff. $147 $124 $93 $158 $164 $171 a) Calculate ̅ , s2 and s for the expense data. b) Assume that the distribution of expenses is approximately normally distributed. Calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all expenses by the sales office. c) If a member of the sales office submits a receipt with the amount of $190, should this expense be considered unusually high? Explain your answer. d) Compute and interpret the z-score for each of the six expenses. Question 2 A survey presents the results of a concept study for the taste of new food. Three hundred consumers between 18 and 49 years old were randomly selected. After sampling the new cuisine, each was asked to rate the quality of food. The rating was made on a scale from 1 to 5, with 5 representing “extremely agree with the quality” and with 1 representing “not at all agree with the new food.” The results obtained are given in Table 1. Estimate the probability that a randomly selected 18- to 49-year-old consumer a) Would give the phrase a rating of 4. b) Would give the phrase a rating of 3 or higher. c) Is in the 18–26 age group; the 27–35 age group; the 36–49 age group. d) Is a male who gives the phrase a rating of 5. e) Is a 36- to 49-year-old who gives the phrase a rating of 2. f) Estimate the probability that a randomly selected 18- to 49-year-old consumer is a 27- to 49-year-old who gives the phrase a rating of 3. g) Estimate the probability that a randomly selected 18- to 49-year-old consumer would 1) give the phrase a rating of 2 or 4 given that the consumer is male; 2) give the phrase a rating of 4 or 5 given that the consumer is female. Based on the results of parts 1 and 2, is the appeal of the phrase among males much different from the appeal of the phrase among females? Explain. h) Give the phrase a rating of 4 or 5, 1) given that the consumer is in the 18–26 age group; 2) given that the consumer is in the 27–35 age group; 3) given that the consumer is in the 36–49 age group. Table 1. Gender Age Group Rating Total Male Female 18-26 27-35 36-49 Extremely Appealing (5) 151 68 83 48 66 37 (4) 91 51 40 36 36 19 (3) 36 21 15 9 12 15 (2) 13 7 6 4 6 3 Not at all appealing(1) 9 3 6 4 3 2 Question 3 Based on the reports provided by the brokers, it is concluded that the annual returns on common stocks are approximately normally distributed with a mean of 17.8 percent and a standard deviation of 29.3 percent. On the other hand, the company reports that the annual returns on tax-free municipal bonds are approximately normally distributed with a mean return of 4.7 percent and a standard deviation of 10.2 percent. Find the probability that a randomly selected a) Common stock will give a positive yearly return. b) Tax-free municipal bond will give a positive yearly return. c) Common stock will give more than a 13 percent return. d) Tax-free municipal bond will give more than a 11.5 percent return. e) Common stock will give a loss of at least 7 percent. f) Tax-free municipal bond will give a loss of at least 10 percent. Question 4 Based on a sample of 176 workers, it is estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. It is also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. We randomly select a sample of 100 workers. a) What is the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days? Assume σ equals 1.3 days. b) What is the probability that the average amount of unpaid time lost during a three-month period for the 100 workers will exceed 1.5 days? Assume σ equals 1.8 days. c) A sample of 100 workers is randomly selected. Suppose the sample mean amount of unpaid time lost during a three-month period actually exceeds 1.5 days. Would it be reasonable to conclude that the mean amount of unpaid time lost has increased above the previously estimated 1.0 day? Explain. Assume σ still equals 1.8 days.

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