Periodically, the Federal Trade Commission (FTC) monitors the pricing accuracy o

Question

Periodically, the Federal Trade Commission (FTC) monitors the pricing accuracy of electronic checkout scanners at stores to ensure consumers are charged the correct price at checkout. A past study of over 100,000 items found that one of every 30 items is priced incorrectly by the scanners. Suppose the FTC randomly selects 45 items at a retail store and check the accuracy of the scanner price at each. Find the following probabilities with and without the Poisson approximation to the binomial distribution. What is the probability that exactly one of the 45 items is priced incorrectly by the scanner? What is the probability that at most two of the 45 items is priced incorrectly by the scanner?

Explanation / Answer

PROBABILITY THAT IT WILL BE INACCURATE IN THE SCANNER = 1/30 = 0.033

PROBABILITY THAT IT WILL BE ACCURATE = 0.999

A) P(X=1 INCORRECT) = 45C1*(0.033)^1*(0.966)^44 = 0.34

B) PROBABILITY ( AT MOST 2 INCORRECT) = P(0)+P(1)+P(2)

P(0 IN CORRECT) = 0.966^45 = 0.210

P(2 INCORRECT) = 45C2(0.033)^2*(0.966)^43 = 0.243

HENCE ANSWER WILL BE = 0.210+0.340 + 0.243 = 0.793

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