Downloading apps to your cell phone. According to a study, nearly 40% of adult cell phone owners have downloaded an application (“app”) to their cell phone. The accompanying 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.

Number of Apps Used, x p(x)

0 .30 1 .24 2 .06 3 .06 4 .05 5 .10 6 .07 7 .05 8 .03 9 .02 10 .02

a. Show that the properties of a probability distribution for a discrete random variable are satisfied.

b. Find P1x 7 32.