A particular telephone number is used to both voice calls and fax messages. Supp

Question

A particular telephone number is used to both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 7 of the calls involve a fax message? (b) What is the probability that exactly 7 of the calls involve a fax message? (c) what is the probability that at least 7 of the calls involve a fax message? (d) What is the probability that more than 7 of the calls involve a fax message?

Explanation / Answer

sample size, n = 25, probability of success for fax, p = 25% = 0.25

The formula shown are for excel.

a) Number of success, k = 9, Using binomial distribution
P(X 9) -> "=BINOM.DIST(9,25,0.25,TRUE)" = 0.927

b) P(X=7) = nCk * pk * (1-p)n-k = 25C7 * 0.257 * 0.7518 = 0.165 ( "=BINOM.DIST(7,25,0.25,FALSE)" )

c) P(X>=7) -> "=1 - BINOM.DIST(6,25,0.25,TRUE)" = 0.439

d) P(X>7) -> "=1 - BINOM.DIST(7,25,0.25,TRUE)" = 0.273

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