A mail-order company business has six telephone lines. Let X denote the number o

Question

A mail-order company 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. 0 2 4 5 P) 0.12 0.15 0.20 0.25 0.18 0.05 0.05 Calculate the probability of each of the following events. (a) fat most three lines are in use (b) fewer than three lines are in use) (c) Cat 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) () fat least four lines are not in use

Explanation / Answer

a) P(at most 3 lines are in use) = P(0) + P(1) + P(2) + P(3) = 0.12+0.15 + 0.2 + 0.25 = 0.72

b) P(fewer than 3 lines are in use) =  P(0) + P(1) + P(2) = 0.12+0.15 + 0.2 = 0.47

c) P(atleast 3 lines are in use) = P(3) + P(4) + P(5) + P(6) = 0.25 + 0.18 + 0.05 + 0.05 = 0.53

d) P(between 2 and 5 lines, inclusive are in use) = P(2) + P(3) + P(4) + P(5) = 0.2 +0.25 + 0.18 + 0.05 = 0.68

e) P(between 2 and 4 lines, inclusive are not in use) =  P(0) + P(1) + P(5) + P(6) = 0.12 + 0.15 + 0.05 + 0.05 = 0.37

f) P(atleast 4 lines are not in use) = 1 - P(at least 4 lines are in use) = 1 - [P(4) + P(5) + P(6)] = 1- [0.18 +0.05 +0.05] = 1- 0.19 = 0.72  

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