7.35 A local television station sells 15-second, 30-second, and 60-second advertising spots. Let x denote the length of a randomly selected commercial appearing on this station, and suppose that the probability distribution of x is given by the following table:

x 15 30 60 p(x) .1 .3 .6

a. Find the average length for commercials appearing on this station.

b. If a 15-second spot sells for $500, a 30-second spot for $800, and a 60-second spot for $1000, find the average amount paid for commercials appearing on this station. (Hint: Consider a new variable, y 5 cost, and then find the probability distribution and mean value of y.)