A particular telephone number is used to receive both voice calls and fax messag

Question

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.)

(a) What is the probability that exactly 7 of the calls involve a fax message?

(b) What is the probability that at most 2 of the calls involve a fax message?

(c) What is the probability that more than 2 of the calls involve a fax message? (d) What is the expected number of call involving a fax message and it standard deviation?

Explanation / Answer

Answer:

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.)

Binomial distribution used.

n=20, p=0.20

P(X=x) = (nCx) px (1-p)n-x

(a) What is the probability that exactly 7 of the calls involve a fax message?

P( x=7) = 0.055

(b) What is the probability that at most 2 of the calls involve a fax message?

P( x 2) = P( x=0)+P( x=1)+P( x=2)

= 0.0115+ 0.0576+ 0.1369

=0.206

(c) What is the probability that more than 2 of the calls involve a fax message?

P( x >2) =1- P( x 2) = 1-0.206

=0.794

(d) What is the expected number of call involving a fax message and it standard deviation?

Expectation = np = 4

Variance = np(1 - p) = 3.2

Standard deviation = 1.789

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