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

Question

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 probabilities of the following events given below. {at most three lines are in use} ____ {fewer than three lines are in use} _______ {at least three lines are in use} _____ {between two and five lines, indusive, are in use} ________ {between two and four lines, indusive, are not in use} ________ {at least four lines are in use} ________

Explanation / Answer

a) P(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) P(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

c) P(at least three lines are in use) = P(x>=3)

=P(x=3)+P(x=4)+P(x=5)+P(x=6)

=0.25+0.20+0.05+0.05

=0.55

d)P(between two and five lines,inclusive are in use)=P(2<=x<=5)

=P(x=2)+P(x=3)+P(x=4)+P(x=5)

=0.2+0.25+0.20+0.05

=0.70

e)P(between two and four lines,inclusive are not in use) =P(2<x<4)

=P(x=3)

=0.25

f) P(at least four lines are not in use) = 1- P(x>=4)

=P(x<=3)

from a) part

P(x<=3) = 0.70

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