and fax suppose that 20% of th-incoming cals invoetax messages, consider a sangi

Question

and fax suppose that 20% of th-incoming cals invoetax messages, consider a sangiu of 20 anooming caguund you ammers so three A particular telephone number is used to receive both voike decimal places) enessages. ) What is the probability that at most 4 of the calls involve a fax message? (b) What is the probability that esxaectly 4 of the calls Involve a fax message? What is the probability that at least 4 of the calls Involve a tax message? ) What is the probability that more than 4 of the calfis invoive a fax message? You may need to use the appropriate table in the Appendix of Tables to answer this question Need Help? Lh..Cilyan.h

Explanation / Answer

This is bionomial(n,p) distribution where n = 20 , p = 0.20

f(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 - { 20C0 0.200 0.8020 +  20C1 0.201 0.8019 +  20C2 0.202 0.8018 }

= 1 - 0.411

= 0.589

d)

p(x>4) = 1 - p(x<=4)

= 1 - 0.630

= 0.370

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