About 30 of all US adults try to adjust their income deducti

About 30% of all U.S. adults try to adjust their income deductions so that they either pay the IRS less or get more money back. You work for the IRS and 256 tax returns just arrived that need to be processed in the next few days. What is the probability that between 60 and 65 of the returns have deductions that have been adjusted?

Solution

p =0.3

n = 256

This is binominal distribution,

P(x=r) = nCr * p^r * q^(n-r)

From that, following table is made.

P(60<=x<=65) = P(x=60) + P(x=61) + ............+P(x=65)

P(60<=x<=65) = 0.0519 (summation from table)