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Oakdale Furniture Company uses a special type of woodworking glue in the assembly of its furniture. During the past 36 weeks, the following amounts of glue (in gallons) were used by the company: 25 38 26 31 21 46 29 19 35 39 24 21 17 42 46 19 50 40 43 34 31 51 36 32 18 29 22 21 24 39 46 31 33 34 30 30 a. Compute the mean and the standard deviation of this sample. b. Consider the following class intervals for the number of gallons used each week: Less than 20. 20-27. 28–33. 34–37. 38–43. More than 43. Determine the proportion of data points that fall into each of these intervals. Compare these proportions to the probabilities that a normal variate with the mean and the standard deviation you computed in part (a) falls into each of these intervals. Based on the comparison of the observed proportions and those obtained from assuming a normal distribution, would you conclude that the normal distribution provides an adequate fit of these data? (This procedure is essentially the same as a chi-square goodness-of-fit test.) c. Assume that the numbers of gallons of glue used each week are independent random variables, having the normal distribution with mean and standard deviation computed in part (a). What is the probability that the total number of gallons used in six weeks does not exceed 200 gallons? (Hint: The mean of a sum of random variables is the sum of the means and the variance of a sum of independent random variables is the sum of the variances.)

Oakdale Furniture Company uses a special type of woodworking glue in the assembly of its furniture. During the past 36 weeks, the following amounts of glue (in gallons) were used by the company: 25 38 26 31 21 46 29 19 35 39 24 21 17 42 46 19 50 40 43 34 31 51 36 32 18 29 22 21 24 39 46 31 33 34 30 30 a. Compute the mean and the standard deviation of this sample. b. Consider the following class intervals for the number of gallons used each week: Less than 20. 20-27. 28–33. 34–37. 38–43. More than 43. Determine the proportion of data points that fall into each of these intervals. Compare these proportions to the probabilities that a normal variate with the mean and the standard deviation you computed in part (a) falls into each of these intervals. Based on the comparison of the observed proportions and those obtained from assuming a normal distribution, would you conclude that the normal distribution provides an adequate fit of these data? (This procedure is essentially the same as a chi-square goodness-of-fit test.) c. Assume that the numbers of gallons of glue used each week are independent random variables, having the normal distribution with mean and standard deviation computed in part (a). What is the probability that the total number of gallons used in six weeks does not exceed 200 gallons? (Hint: The mean of a sum of random variables is the sum of the means and the variance of a sum of independent random variables is the sum of the variances.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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In the given problem, what other probability distributions might accurately describe Oakdale’s weekly usage of glue?

Oakdale Furniture Company uses a special type of woodworking glue in the assembly of its furniture. During the past 36 weeks, the following amounts of glue (in gallons) were used by the company: 25 38 26 31 21 46 29 19 35 39 24 21 17 42 46 19 50 40 43 34 31 51 36 32 18 29 22 21 24 39 46 31 33 34 30 30 a. Compute the mean and the standard deviation of this sample. b. Consider the following class intervals for the number of gallons used each week: Less than 20. 20-27. 28–33. 34–37. 38–43. More than 43. Determine the proportion of data points that fall into each of these intervals. Compare these proportions to the probabilities that a normal variate with the mean and the standard deviation you computed in part (a) falls into each of these intervals. Based on the comparison of the observed proportions and those obtained from assuming a normal distribution, would you conclude that the normal distribution provides an adequate fit of these data? (This procedure is essentially the same as a chi-square goodness-of-fit test.) c. Assume that the numbers of gallons of glue used each week are independent random variables, having the normal distribution with mean and standard deviation computed in part (a). What is the probability that the total number of gallons used in six weeks does not exceed 200 gallons? (Hint: The mean of a sum of random variables is the sum of the means and the variance of a sum of independent random variables is the sum of the variances.)
Transcribed Image Text:Oakdale Furniture Company uses a special type of woodworking glue in the assembly of its furniture. During the past 36 weeks, the following amounts of glue (in gallons) were used by the company: 25 38 26 31 21 46 29 19 35 39 24 21 17 42 46 19 50 40 43 34 31 51 36 32 18 29 22 21 24 39 46 31 33 34 30 30 a. Compute the mean and the standard deviation of this sample. b. Consider the following class intervals for the number of gallons used each week: Less than 20. 20-27. 28–33. 34–37. 38–43. More than 43. Determine the proportion of data points that fall into each of these intervals. Compare these proportions to the probabilities that a normal variate with the mean and the standard deviation you computed in part (a) falls into each of these intervals. Based on the comparison of the observed proportions and those obtained from assuming a normal distribution, would you conclude that the normal distribution provides an adequate fit of these data? (This procedure is essentially the same as a chi-square goodness-of-fit test.) c. Assume that the numbers of gallons of glue used each week are independent random variables, having the normal distribution with mean and standard deviation computed in part (a). What is the probability that the total number of gallons used in six weeks does not exceed 200 gallons? (Hint: The mean of a sum of random variables is the sum of the means and the variance of a sum of independent random variables is the sum of the variances.)
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