Business Franchise: Shopping Center Chances: Risk and Odds

Chapter , Problem 22

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Business Franchise: Shopping Center Chances: Risk and Odds in Everyday Life, by James Burke, reports that only 2% of all local franchises are business failures. A Colorado Springs shopping complex has 137 franchises (restaurants, print shops, convenience stores, hair salons, etc.).

(a) Let r be the number of these franchises that are business failures. Explain why a Poisson approximation to the binomial would be appropriate for the random variable r. What is n? What is p? What is \(\lambda\) (rounded to the nearest tenth)?

(b) What is the probability that none of the franchises will be a business failure?

(c) What is the probability that two or more franchises will be business failures?

(d) What is the probability that four or more franchises will be business failures?

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