Question 182563: I need some help solving this problem..
USE THE NORMAL APPROXIMATION OF THE BINOMIAL PROBABILITY
DISTRIBUTION TO SOLVE THE PROBLEM BELOW.
DeKorte Telemarketing Inc. is considering purchasing a machine that randomly
selects and automatically dials telephone numbers. It makes most of its calls
during the evening, so calls to business phones are wasted. The manufacturer of
the machine claims that their programming reduces the calling to business phones
to 15 percent of all calls. To test this claim, the Director of Purchasing at
DeKorte programmed the machine to select a sample of 150 phone numbers.
What is the probability that more than 30 of the phone selected are that of a
business, assuming the manufacturer’s claim is correct?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! USE THE NORMAL APPROXIMATION OF THE BINOMIAL PROBABILITY
DISTRIBUTION TO SOLVE THE PROBLEM BELOW.
DeKorte Telemarketing Inc. is considering purchasing a machine that randomly
selects and automatically dials telephone numbers. It makes most of its calls
during the evening, so calls to business phones are wasted. The manufacturer of
the machine claims that their programming reduces the calling to business phones
to 15 percent of all calls. To test this claim, the Director of Purchasing at
DeKorte programmed the machine to select a sample of 150 phone numbers.
What is the probability that more than 30 of the phone selected are that of a
business, assuming the manufacturer’s claim is correct?
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u = np = 150*0.15 = 22.5
sigma = sqrt(npq) = sqrt(22.5*0.85) = sqrt(19.125) = 4.373
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Normal Approx Approach:
P(31 < x <= 150) = normal cdf(31,150,22.5,4.373) = 0.324...
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Cheers,
Stan H.
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