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Chapter 7: Q.57 (page 455)
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks mote and more Normal." ls the student right? Explain your answer.
The student is not right
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Songs on an iPod David's iPod has about songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of seconds and a standard deviation of seconds.
(a) Explain why you cannot safely calculate the probability that the mean play time is more than minutes seconds for an SRS of songs.
(b) Suppose we take an SRS of songs instead. Explain how the central limit theorem allows us to find the probability that the mean playtime is more than seconds. Then calculate this probability. Show your work.
A machine is designed to fill -ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is ounces with a standard deviation of ounces. Assume that the machine is working properly. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then of the observations should occur in which interval?
(a) to ounces
(b) to ounces
(c) to ounces
(d) to ounces
(e) None of the above
When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes ispounds with a standard deviation of pounds, the mean weight of the packing material is pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is pounds with a
standard deviation of pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?
(a)
(b)
(c)
(d)
(e)
Graph the population distribution. Identify the individuals, the variable, and the parameter of interest.
In the language of government statistics, you are 鈥渋n the labor force鈥� if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged years and over in a recent year. The table entries are counts in thousands of people.
If you know that a randomly chosen person years of age or older is a college graduate, what is the probability that he or she is in the labor force? Show your work.
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