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:

\(A= np =137(0.02) = 2.74\)