Public Health and Nutrition
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. 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
|
X
|
10
|
12
|
15
|
20
|
25
|
30
|
|
P(x)
|
0.30
|
0.25
|
0.15
|
0.12
|
0.10
|
0.08
|
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?