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 nvolve ax messages, and consider a sample of 20 ncoming calls. Round your answers to three decimal places. a) What is the probability that at most 4 of the calls involve a fax message? what is the probability that exacdy 4 of the calls involve a fax message? (c) what is the probability that at least 4 of the calls invole fax message? (d) what is the probability that more than 4 of the calls involve a fax message? You may rneed to use the appropriate table in the Appendix of Tables to answer this question

Explanation / Answer

X ~ Binomial(n,p) = Binomial(20,0.20)

Binomial probability distribution is

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

a)

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

= 20C0 0.200 0.8020 + 20C1 0.201 0.8019 + 20C2 0.202 0.8018 + 20C3 0.203 0.8017 + 20C4 0.204 0.8016

= 0.630  

b)

P( X = 4) =  20C4 0.204 0.8016

= 0.218

c)

P( X >= 4) = 1 - P( X <= 3)

= 1 - { P( X = 0) + P( X = 1) + P( X = 2) + P( X = 3) }

= 1 - { 20C0 0.200 0.8020 + 20C1 0.201 0.8019 + 20C2 0.202 0.8018 + 20C3 0.203 0.8017 }

= 0.589

d)

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

= 1 - 0.630 ( Probability for P( X<= 4 ) calculated in part a )

= 0.370

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