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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WEEKLY ASSIGNMENT #2 YOU 1. Verify for the Cobb-Douglas production function P(L;K) = 1:01L:75K:25 that the production will be doubled if both the amount of labor and the amount of capital are doubled. How much must you increase capital K to double production? How much must you increase labor by to double production? 1 2. Let F(x; y) = 1+ p 4 ? y2. Evaluate F(3; 1). Find and sketch the domain of F. Find the range of F. 2 3. Draw a contour map of the function showing several level curves. (a) g(x; y) = x2 ? y2 (b) s(x; y) = y=(x2 + y2) 3 4. Find the limit if it exists or show that the limit does not exist. You do not have to use the epsilon delta method so it will either be “obviously” continuous or you will have to show that it is not by finding two paths which give different results. (a) lim (x;y)!(2;?1) x2y + xy2 x2 ? y2 (b) lim (x;y)!(0;0) x4 ? 4y2 x2 + 2y2 (c) lim (x;y)!(0;0) xy p x2 + y2 4 5. The temperature T at a location in the Norther Hemisphere depends on the longitude x, the latitude y, and the time t. What are the meaning of the partial derivatives @T=@t; @T=@x; @T=@y? Moscow lies at 46:73N; 117W. Suppose that at 9 am on January 1st the wind is blowing hot air to the northeast so the air to the west and south is warm, and the air to the north and east is cooler. Would you expect fx(117; 4673; 9); fy(117; 4673; 9); ft(117; 4673; 9) to be positive negative or positive? 5 6. Find the first partial derivatives of the following functions. (a) f(x; y) = x4 + 5xy3 (b) g(x; y) = t2e?t (c) h(s; t) = ln(s + t2) (d) i(x; y) = x y (e) R(p; q) = arctan pq2 6 7. Find @z=@x and @z=@y for the following, assuming that f and g are differentiable single variable functions Hint: Your answer should use f0 and/or g0. z = f(x)g(y) ; z = f(x=y) 7

## WEEKLY ASSIGNMENT #2 YOU 1. Verify for the Cobb-Douglas production function P(L;K) = 1:01L:75K:25 that the production will be doubled if both the amount of labor and the amount of capital are doubled. How much must you increase capital K to double production? How much must you increase labor by to double production? 1 2. Let F(x; y) = 1+ p 4 ? y2. Evaluate F(3; 1). Find and sketch the domain of F. Find the range of F. 2 3. Draw a contour map of the function showing several level curves. (a) g(x; y) = x2 ? y2 (b) s(x; y) = y=(x2 + y2) 3 4. Find the limit if it exists or show that the limit does not exist. You do not have to use the epsilon delta method so it will either be “obviously” continuous or you will have to show that it is not by finding two paths which give different results. (a) lim (x;y)!(2;?1) x2y + xy2 x2 ? y2 (b) lim (x;y)!(0;0) x4 ? 4y2 x2 + 2y2 (c) lim (x;y)!(0;0) xy p x2 + y2 4 5. The temperature T at a location in the Norther Hemisphere depends on the longitude x, the latitude y, and the time t. What are the meaning of the partial derivatives @T=@t; @T=@x; @T=@y? Moscow lies at 46:73N; 117W. Suppose that at 9 am on January 1st the wind is blowing hot air to the northeast so the air to the west and south is warm, and the air to the north and east is cooler. Would you expect fx(117; 4673; 9); fy(117; 4673; 9); ft(117; 4673; 9) to be positive negative or positive? 5 6. Find the first partial derivatives of the following functions. (a) f(x; y) = x4 + 5xy3 (b) g(x; y) = t2e?t (c) h(s; t) = ln(s + t2) (d) i(x; y) = x y (e) R(p; q) = arctan pq2 6 7. Find @z=@x and @z=@y for the following, assuming that f and g are differentiable single variable functions Hint: Your answer should use f0 and/or g0. z = f(x)g(y) ; z = f(x=y) 7

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Que 5: the temperature T at a location in the Norther Hemisphere depends on the longitude x, the latitude y, and the time t. what are the meaning of the partial derivatives ∂T/∂t, ∂T/∂x,∂T/∂y ? Moscow lies at 46.73 0 N, 117 0 W. suppose that at 9 am on January 1st the wind is blowing hot air to the northeast so the air to the west and south is warm and the air to the north and east is cooler. Would you expect fx (46.73 0 , 117 0, 9), fy (46.73 0 , 117 0, 9) to be positive negative or positive?

## Que 5: the temperature T at a location in the Norther Hemisphere depends on the longitude x, the latitude y, and the time t. what are the meaning of the partial derivatives ∂T/∂t, ∂T/∂x,∂T/∂y ? Moscow lies at 46.73 0 N, 117 0 W. suppose that at 9 am on January 1st the wind is blowing hot air to the northeast so the air to the west and south is warm and the air to the north and east is cooler. Would you expect fx (46.73 0 , 117 0, 9), fy (46.73 0 , 117 0, 9) to be positive negative or positive?

Sometimes during embryonic development, neural tube defects occur, and they can result in which of the following? Question 9 options: Spina bifida Down syndrome Klinefelter’s syndrome YY syndrome

## Sometimes during embryonic development, neural tube defects occur, and they can result in which of the following? Question 9 options: Spina bifida Down syndrome Klinefelter’s syndrome YY syndrome

Sometimes during embryonic development, neural tube defects occur, and they … Read More...
The current recommendation for most women, after becoming sexually active or starting at age 21, is to have a Pap smear done Question 9 options: once every year once every 6 months once every 3 years once every 5 years