Problem: IRS will audit 2 million taxpayers. Plus 1 million taxpayers will be audited by mail. Assume 100 million total taxpayers. Find the probability that in a random sample of 50 taxpayers there will be one audit and one mail-audit.
My approach:
For the audit: Used Poisson distribution with mu = 1 and x = 1.
P(1) = 1^1 * e^(-1) / 1! = 0.368.
For the mail-audit, I assumed the audit and mail-audit are independent, so I can use Poisson again with mu = 0.5 and x = 1. I get 0.303.
For both events, multiply, yielding 0.112.
What if I assume that the IRS will exclude auditees from mail-a

Question

Problem: IRS will audit 2 million taxpayers.  Plus 1 million taxpayers will be audited by mail.  Assume 100 million total taxpayers.  Find the probability that in a random sample of 50 taxpayers there will be one audit and one mail-audit.
My approach:
For the audit: Used Poisson distribution with mu = 1 and x = 1.
P(1) = 1^1 * e^(-1) / 1! = 0.368.
For the mail-audit, I assumed the audit and mail-audit are independent, so I can use Poisson again with mu = 0.5 and x = 1.  I get 0.303.
For both events, multiply, yielding 0.112.
What if I assume that the IRS will exclude auditees from mail-a

perl · Answer

hmm , does the problem say to use Poisson

anonymous · Answer

Not explicitly, but based on the section where the problem was presented and the rules given in the text, it seems that Poisson was an acceptable approximation to the Binomial.  n = 50.  Although p = 0.01 is a little close to zero.