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.
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?
A bill introduced into the Virginia State Senate stipulated that the owner of a tanning facility must identify and document the skin type of every customer, and must advise every customer of the maximum time of recommended exposure in the tanning device.13 Past records indicate that most sessions range from 10 to 30 minutes. Suppose the duration of a tanning session (in minutes) at the Solar Planet tanning facility in Herendon, Virginia, is a discrete random variable with probability distribution given in the table below.
a. Find the mean, variance, and standard deviation of the duration of a tanning session time.
b. Find the probability that a randomly selected session has a duration within one standard deviation of the mean.
c. Find the probability that a randomly selected session has a duration within two standard deviations of the mean.
d. Suppose a sunlamp lasts for 100 hours. After approximately how many tanning sessions will the sunlamp have to be replaced?