A particular telephone number is used to receive both voice calls and 25 incomin

Question

A particular telephone number is used to receive both voice calls and 25 incoming calls. (Round your answers to three decimal places.) x messages. Suppose at 2 % of the incoming calls in o ax messages and consider a ample o (a) What is the probability that at most 6 of the calls involve a fax message? (b) What is the probability that exactly 6 of the calls involve a fax message? (c) What is the probability that at least 6 of the calls involve a fax message? d) What is the probability that more than 6 of the calls involve a fax message? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read ItTalk to a Tutor

Explanation / Answer

p = 0.25

n = 25

P(X = x) = 25Cx * 0.25x * (1 - 0.25)25-x

a) P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

                  = 25C0 * 0.250 * 0.7525 + 25C1 * 0.251 * 0.7524 + 25C2 * 0.252 * 0.7523 + 25C3 * 0.253 * 0.7522 + 25C4 * 0.254 * 0.7521 + 25C5 * 0.255 * 0.7520 + 25C6 * 0.256 * 0.7519

                  = 0.561

b) P(X = 6) = 25C6 * 0.256 * 0.7519 = 0.183

c) P(X > 6) = 1 - P(X < 6)

                  = 1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

                  = 1 - [25C0 * 0.250 * 0.7525 + 25C1 * 0.251 * 0.7524 + 25C2 * 0.252 * 0.7523 + 25C3 * 0.253 * 0.7522 + 25C4 * 0.254 * 0.7521 + 25C5 * 0.255 * 0.7520 ]

                  = 1 - 0.378

                  = 0.622

d) P(X > 6) = 1 - P(X < 6) = 1 - 0.561 = 0.439

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