7.34 Suppose that for a given computer salesperson, the probability distribution of x 5 the number of systems sold in 1 month is given by the following table:

x 1 2 3 4 5 6 7 8 p(x) .05 .10 .12 .30 .30 .11 .01 .01

a. Find the mean value of x (the mean number of systems sold).

b. Find the variance and standard deviation of x.

How would you interpret these values?

c. What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

d. What is the probability that the number of systems sold is more than 2 standard deviations from the mean? (Hint: See Example 7.13.)