According to the IRS 11 of tax returns will be audited next

According to the IRS, 1.1% of tax returns will be audited next year. A random sample of 40 tax returns was selected. Use the Poisson distribution to approximate the binomial distribution to determine the probability that two or three of these tax returns will be audited

Solution

Given X~Poisson(mean=n*p=40*0.011=0.44)

P(X=x)=(0.44^x)*exp(-0.44)/x!

So the probability that more than two of these tax returns will be audited is

P(X>2)=1-P(X=0)-P(X=1)-P(X=2)

=1-(0.44^0)*exp(-0.44)/1-(0.44^1)*exp(-0.44)/1-(0.44^2)*exp(-0.44)/2

= 0.01024483