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.)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.16P

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Question

a. Consider the Oakdale Furniture Company described in the given problem. Under what circumstances might the major portion of the usage of the glue be predictable?
b. If the demand were predictable, would you want to use a probability law to
describe it? Under what circumstances might the use of a probability model of demand be justified even if the demand could be predicted exactly?

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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