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

Armorikam

Armorikam

Answered question

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)?

Answer & Explanation

krolaniaN

krolaniaN

Skilled2021-06-12Added 86 answers

Given:
a=137
p=2
We can approximatethe binomial distribution with the Poisson distribution, if n100 and np<10.
137100
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
A is the product of the sample size n and the probability p:
A=np=137(0.02)=2.74

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