s O -D points MendStat14 &E08; Suppose that the IRS assigns auditing rates 0.35%

Question

s O -D points MendStat14 &E08; Suppose that the IRS assigns auditing rates 0.35%. state by randomly selecting 50 auditing percentages from a normal di tribution with a mean equal to l 65% and a standard din ution of 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 tar returns adted? (Rand your anne te three deom/pion.) (c) 1s it likely that as many as 16 of the 50 states win have more than 2% of their income tax returns audited. O Because x 16 has a z-score of at least 2, it is unlikely that as many as 16 of the so states will have more than 2% of thair income tax returns audited O Because x-16 has a z. score less than 2, it is unikely that as many as 16 of the so states will have more than 2% of their income tax returns audted. Because x " 16 has a z-score less than 2·it is likely that as many as 16 of the 50 states will have more than 2% of their ncome tax returns audited. Because x = 16 has a z-score of at least 2, it is lkely that as many as 16 of the 50 states wit have more than 2% of their income tax returns audited. You may need to use the appropriate appendix table or technology to answer this question

Explanation / Answer

Here mean auditing rater per state = 1.65%

standard deviation of audisting rate per state = 0.35%

(A) Here x is the probability that a particular state would be more than 2% of its tax return audited.

Pr(x > 2% ) = NORMAL (x > 2% ; 1.65%, 0.35%) = 1- NORM(x < 2% ; 1.65%; 0.35%)

Z = (2 - 1.65)/0.35 = 1

Pr(x > 2% ) = NORMAL (x > 2% ; 1.65%, 0.35%) = 1- NORM(x < 2% ; 1.65%; 0.35%) = 1 - Pr(Z < 1)

= 1 - 0.8413 = 0.1587

(ii) Expected value of x, the number of states that will have more than 2% of their income tax returns audited.

E[x] = 0.1587 * 50 = 7.933

(c) Here Z = (16 - 7.933)/sqrt [0.1587 * 0.8413 * 50] = 8.067/2.5834 = 3.122

HEre it is not liekly that because x = 16 has a z score of at least 2, it is unlikely that as many as 16 of the 50 states will have more than 2% of their income tax returns audited. Option A is correct.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.