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?