The probability that a person with a telephone has an unlistednumber is 0.15. Th

Question

The probability that a person with a telephone has an unlistednumber is 0.15. The district manager of a political action group is phoningpeople urging them to vote. In a district with 416 households, all households havephones. What is the probability that the district manager will find that a. 50 or fewer households in the district have unlistedphone numbers? b. 345 or more have listed phone numbers? c. between 40 and 80 have unlisted numbers? The probability that a person with a telephone has an unlistednumber is 0.15. The district manager of a political action group is phoningpeople urging them to vote. In a district with 416 households, all households havephones. What is the probability that the district manager will find that a. 50 or fewer households in the district have unlistedphone numbers? b. 345 or more have listed phone numbers? c. between 40 and 80 have unlisted numbers?

Explanation / Answer

a. 50 or fewer households in the district have unlistedphone numbers?
P(X<=50) = P((x-)/ <(50-62.4)/7.28)
=P(Z<-1.7)
= 0.0445 (check normal table)

b. 345 or more have listed phone numbers?
X~Normal(=n*p=416*0.85=353.6,=n*p*(1-p)=sqrt(416*0.85*0.15)=7.28)

P(X>345) = P(Z>(345-353.3)/7.28)
=P(Z>-1.14)
=0.8728 (check normal table)

c. between 40 and 80 have unlisted numbers?

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