According to an August 2011 survey by the Pew Internet & American Life Project, nearly 40% of adult cell phone owners have downloaded an application ("app") to their cell phone. The next table gives the probability distribution for x, the number of "apps" used at least once a week by cell phone owners who have downloaded an "app" to their phone. (The probabilities in the table are based on information from the Pew Internet & American Life Project survey.)
Number of "Apps" Used, x p(x)
0 ........................................ .17
1 ........................................ .10
2 ........................................ .11
3 ........................................ .11
4 ........................................ .10
5 ........................................ .10
6 ........................................ .07
7 ........................................ .05
8 ........................................ .03
9 ........................................ .02
10 ........................................ .02
11 ........................................ .02
12 ........................................ .02
13 ........................................ .02
14 ........................................ .01
15 ........................................ .01
16 ........................................ .01
17 ........................................ .01
18 ........................................ .01
19 .........................................005
20 .........................................005
a. Show that the properties of a probability distribution for a discrete random variable are satisfied.
b. Find P(x ≥ 10).
c. Find the mean and variance of x.
d. Give an interval that will contain the value of x with a probability of at least .75.