Refer to Exercise 13, and calculate and graph the cdf F(x). Then use it to calculate the probabilities of the events given in parts (a)–(d) of that problem. Reference Exercise 13 p>A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. Calculate the probability of each of the following events. 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}

Answer : Step 1 of 5 : Given, A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. x P(x) 0 0.10 1 0.15 2 0.20 3 0.25 4 0.20 5 0.06 6 0.04 Step 2 of 5 : a) We have to find the probability of at most three lines are in use P(x3) = P(x = 0) + P(x=1) + P(x=2) + P(x=3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70 0.70 be the probability of at most three lines are in use Step 3 of 5 : b) We have to find the probability of fewer than three lines are in use P(x<3) = P(x = 0) + P(x=1) + P(x=2) = 0.10 + 0.15 + 0.20 = 0.45 0.45 be the probability of fewer than three lines are in use.