Suppose that the IRS assigns auditing rates per state by randomly selecting 50 a

Question

Suppose that the IRS assigns auditing rates per state by randomly selecting 50 auditing percentages from a normal distribution with a mean equal to 1.65% and a standard deviation of 0.35%.

(a) What is the probability that a particular state would have more than 2% of its tax returns audited? (Round your answer to four decimal places.)


(b) What is the expected value of x, the number of states that will have more than 2% of their income tax returns audited? (Round your answer to three decimal places.)


(c) Is it likely that as many as 11 of the 50 states will have more than 2% of their income tax returns audited?

Explanation / Answer

here mean=1.65, standard deviation=sd=0.35

we use and calculate standard normal variante z=(x-mean)/sd

answer a) for x=2, z=(2-1.65)/0.35=1

P(x>2)=P(z>1)=1-P(z<1)=1-0.8413=0.1587

answer b) the number of states that will have more than 2% of their income tax returns audited=50*0.1587=7.938(next whole number=8)

expected value of x=8

answer c) No, as the number of states that will have more than 2% of thier income tax returns audited are=8

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