7.107 A business has six customer service telephone lines.

Let x denote the number of lines in use at a specified time. Suppose that the probability distribution of x is as follows:

x 0 1 2 3 4 5 6 p(x) .10 .15 .20 .25 .20 .06 .04 Write each of the following events in terms of x, and then calculate the probability of each one:

a. At most three lines are in use

b. Fewer than three lines are in use

c. At least three lines are in use

d. Between two and five lines (inclusive) are in use

e. Between two and four lines (inclusive) are not in use

f. At least four lines are not in use 7.108 Refer to the probability distribution of the previous exercise.

a. Calculate the mean value and standard deviation of x.

b. What is the probability that the number of lines in use is farther than 3 standard deviations from the mean value?