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Chapter 7: Q.22 (page 428)
An unknown distribution has a mean 12 and a standard deviation of one. A sample size of is taken.
Let = the object of interest.
What is the mean of ?
The mean of.
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Yoonie is a personnel manager in a large corporation. Each month she must review of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of hours. Let 围 be the random variable representing the time it takes her to complete one review. Assume 围 is normally distributed. Let be the random variable representing the meantime to complete the reviews. Assume that the 16 reviews represent a random set of reviews.
Find the probability that the mean of a month鈥檚 reviews will take Yoonie from to hrs. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability.
a.
b. P(________________) = _______
. Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let be the random variable of sums. For parts, c through f, sketch the graph, shade the region, label and scale the horizontal axis for , and find the probability.
a. Sketch the distributions of X and on the same graph.
b.
c.
d. Find the 30th percentile for the mean.
e.
f.
g.
h. Find the minimum value for the upper quartile for the sum.
i. $
66. In 1940 the average size of a U.S. farm was 174 acres. Let's say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940.
a. In words, X=
b. In words, =
c.
d. The IQR for is from acres to acres.
According to Boeing data, the airliner carries passengers and has doors with a height of inches. Assume for a certain population of men we have a mean height of inches and a standard deviation of inches.
a. What doorway height would allow of men to enter the aircraft without bending?
b. Assume that half of the passengers are men. What mean doorway height satisfies the condition that there is aprobability that this height is greater than the mean height of men?
c. For engineers designing the , which result is more relevant: the height from part a or part b? Why?
81. The percentile sample average wait time (in minutes) for a sample of 100 riders is:
a.
b.
c.
d.
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