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Chapter 7: Q. 7.1 (page 403)
An unknown distribution has a mean of 45 and a standard deviation of eight. Samples of size are drawn randomly from the population. Find the probability that the sample mean is between and .
the probability that the sample mean is
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The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be per year with a standard deviation of . We randomly survey residents of that country.
a. In words,
b. In words,
c.
d. How is it possible for the standard deviation to be greater than the average?
e. Why is it more likely that the average of the residents will be from to than from ?
Salaries for teachers in a particular elementary school district are normally distributed with a mean of and a standard deviation of . We randomly survey ten teachers from that district.
a. In words,
b.
c. In words,
d.
e. Find the probability that the teachers earn a total of over .
f. Find the percentile for an individual teacher's salary.
g. Find the percentile for the sum of ten teachers' salary.
h. If we surveyed teachers instead of ten, graphically, how would that change the distribution in part d?
i. If each of the teachers received a raise, graphically, how would that change the distribution in part b?
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 reviews represent a random set of reviews.
Find the probability that one review will take Yoonie from to hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability
b. P(________ <x< ________) = _______
The length of songs in a collector鈥檚 iTunes album collection is uniformly distributed from two to minutes. Suppose we randomly pick five albums from the collection. There are a total of songs on the five albums.
a. In words,
b.
c. In words,
d.
e. Find the first quartile for the average song length, .
f. The IQR (interquartile range) for the average song length, , is from ___ - ___.
NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of hours with a standard deviation of hours. Your statistics class questions this claim. As a class, you randomly select batteries and find that the sample mean life span is hours. If the process is working properly, what is the probability of getting a random sample of batteries in which the sample mean lifetime is hours or less? Is the company鈥檚 claim reasonable?
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