Suppose that the IRS assigns auditing rates per state by randomly selecting 50 auditing percentages from a normal distribution with a mean equal to 1.75% and a standard deviation of 0.25%.
a) What is the probability that a particular state would have more than 2% of its tax returns audited?
b) What is the expected value of x, the number of states that will have more than 2% of their income tax returns audited?
c) Is it likely that as many as 11 of the 50 states will have more than 2% of their income tax returns audited?