Answer/Work out every part please! A particular telephone number is used to rece

Question

Answer/Work out every part please!

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 at most 4 of the calls involve a fax message? (b) What is the probability that exactly 4 of the calls involve a fax message? (c) What is the probability that at least 4 of the calls involve a fax message? (d) What is the probability that more than 4 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 it Talk to a Tutor

Explanation / Answer

n = 20

p = 0.2

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

= 20C0 * (0.2)^ 0 * (0.8)^20 + 20C1 * (0.2)^ 1 * (0.8)^19 + 20C2 * (0.2)^ 2 * (0.8)^18 + 20C3 * (0.2)^ 3 * (0.8)^17 + 20C4 * (0.2)^ 4 * (0.8)^16

                   = 0.6296

b) P(X = 4) = 20C4 * (0.2)^ 4 * (0.8)^16 = 0.2182

c) P(X > 4) = 1 - P(X < 4)

                    = 1 - (P(X = 0) + P(x = 1) + P(X = 2) + P(X = 3))

                    = 1 - ( 20C0 * (0.2)^ 0 * (0.8)^20 + 20C1 * (0.2)^ 1 * (0.8)^19 + 20C2 * (0.2)^ 2 * (0.8)^18 + 20C3 * (0.2)^ 3 * (0.8)^17 )

                    = 1 - 0.4114 = 0.5886

d) P(X > 4) = 1 - P(X < 4)

                  = 1 - 0.6296 = 0.3704

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