Question

Chances: Risk and Odds in Everyday Life, by James Burke, reports that only 2% of all local franchises are business failures. A Colorado Springs shoppi

Random variables
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asked 2021-06-11
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.). 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 λλ (rounded to the nearest tenth)?

Answers (1)

2021-06-12

Given:
\(a= 137\)
\(p=2%=0.02\)
We can approximatethe binomial distribution with the Poisson distribution, if \(\displaystyle{n}\geq100\) and \(np < 10.\)
\(\displaystyle{137}\geq{100}\)
\(np = 137(0.02) = 2.74 < 10\)
Thus it is appropriate to approximate the binomial distribution with the Poisson distribution.
nis the sample size:
\(n=137\)
p is the given rate rewritten as a decimal:
\(p=2%=0.02\)
A is the product of the sample size n and the probability p:
\(A= np =137(0.02) = 2.74\)

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