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
ANSWERED 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 &lambda;&lambda; (rounded to the nearest tenth)? 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:
$$A= np =137(0.02) = 2.74$$