6) A mail-order computer business has six telephone lines. Let X represent the n

Question

6) A mail-order computer business has six telephone lines. Let X represent the number of lines in use at a specified time. Suppose the pmf of X'is given below: 01 2 3 P(x) 0.10 0.15 0.20 0.25 0.20 0.06 0.04 Write, mathematically, the probability with respect to X that is needed for each of the following events, and calculate the probability. (a) at most three lines are n use (b) fewer than 2 lines are in use (c) no more than 4 lines are in use (d) between 2 and 5 lines, inclusively, are in use. (e) at least 4 lines are not in use

Explanation / Answer

6) a) At most three lines are in use

P(x <= 3) = {P(x=0) + P(x=1) + P(x=2) + P(x=3)} = 0.10 + 0.15 + 0.20 + 0.25 = 0.70

b) fewer than 2 lines are in use

P(x < 2) = {P(x=0) + P(x=1)} = 0.10 + 0.15 = 0.25

c) No more than 4 lines are in use. It is same as a) but P(x=4) must be added to it.

P(x<=4) = {(P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4)} = 0.10 + 0.15 + 0.20 + 0.25 + 0.20 = 0.90

d) P(2 <= x <= 5) = {P(x=2) + P(x=3) + P(x=4) + P(x=5)} = 0.20 + 0.25 + 0.20 + 0.06 = 0.71

e) 1 - P(x=4) = 1 - 0.90 = 0.10

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