A particular telephone number is used to receive both voice

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 15 incoming calls.

PART A: What is the expected number of calls among the 15 calls that involve a fax message?

PART B: What is the standard deviation of the number among the 15 calls that involve a fax message?

PART C: What is the probability that EXACTLY ONE call among the 15 that involve a fax message?

PART D: What is the probability that AT LEAST ONE call among the 15 that involve a fax message?

Solution

Given X follows Binomial distribution with n=15 and p=0.25

P(X=x)=15Cx*(0.25^x)*(0.75^(15-x)) for x=0,1,2,...,15

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(A)expected number = n*p= 15*0.25 =3.75

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(B)standard deviation =sqrt(n*p*(1-p))

=sqrt(15*0.25*0.75) =1.677051

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(C) P(X=1) =15C1*(0.25^1)*(0.75^(15-1)) = 0.06681731

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(D) P(X>=1) =1-P(X=0) =0.9866365