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Public Policy and Political Science
Approximately 100 children's products are recalled every year.12 In particular, children's clothing is recalled for a variety of reasons, for example, drawstrings that are too long and pose a hazard, small buttons that may break off and cause choking, and material that fails to meet federal flammability standards. Suppose the number of recalls of children's clothing during a given month is a random variable with probability distribution given in the table below
X
0
1
2
3
4
5
6
P(x)
0.005
0.185
0.275
0.305
0.200
0.020
0.010
a. Find the mean, variance, and standard deviation of the number of recalls of children's clothing during a given month.
b. Suppose the number of recalls in a given month is at least three. What is the probability that the number of recalls that month will be at least five?
c. If the number of recalls in a given month is above more than one standard deviation from the mean, the federal government issues a special warning directed toward parents. What is the probability that a special warning will be issued during a given month?
Suppose that the reported figure is a sample estimate based on 80 randomly chosen homes in this city, and that the population standard deviation was known to be $55,000. Give an 80% confidence interval for the population mean home price.
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