5) In which of the following stories is a binomial approximation to the hypergeo

Question

5) In which of the following stories is a binomial approximation to the hypergeometric valid? Please explain your answer. Please calculate for both the exact hypergeometric (Wolfram Alpha?) and the binomial approximation and compare the answers.

a) At Holloway Gymnasium, there are 2000 fans attending a volleyball game of Purdue vs. Rutgers. The probability that a person attending the game from Rutgers is 1%. What is the probability that out of 110 randomly selected fans, 2 root for Rutgers?

b) At the Brea Mall (Brea, California), there are approximately 200 specialty stores. (The Tippecanoe Mall only has approximately 110 stores.) On a particular day, the probability that a store in the mall does NOT have a sale is 1%. What is the probability that out of 8 stores in the mall that 2 of them do NOT have sales?

Explanation / Answer

for  binomial approximation to the hypergeometric distribution; n/N should be <=0.05 ; where n=sample size

N =population size

a) here n/N =110/2000 =0.055 whcih is higher than 0.05 level ; therefore we can not apply  binomial approximation of the hypergeometric distribution

b) n/N =8/200 =0.04 which is less than 0.05 level and therefore we can apply  binomial approximation of the hypergeometric distribution

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