Studies have shown that about half of all workers who change jobs cash out their 401(k) plans rather than leaving the money in the account to grow. The percentage is much higher for workers with small 401(k) balances. In fact, 87% of workers with 401(k) accounts less than $5,000 opt to take their balance in cash rather than roll it over into individual retirement accounts when they change jobs.
Appendix A Statistical Tables
*(Round your answer to 3 decimal places when calculating using Table A.2.)
**(Round your answer to 4 decimal places.)
a. Assuming that 50% of all workers who change jobs cash out their 401(k) plans, if 16 workers who have recently changed jobs that had 401(k) plans are randomly sampled, what is the probability that more than 10 of them cashed out their 401(k) plan?
b. If 10 workers who have recently changed jobs and had 401(k) plans with accounts less than $5,000 are randomly sampled, what is the probability that exactly 6 of them cashed out?
End of Section Problem 5.16
According to Cerulli Associates of Boston, 30% of all CPA financial advisors have an average client size between $500,000 and $1 million. Thirty-four percent have an average client size between $1 million and $5 million. Suppose a complete list of all CPA financial advisors is available and 18 are randomly selected from that list.
Appendix A Statistical Tables
a. What is the expected number of CPA financial advisors that have an average client size between $500,000 and $1 million? What is the expected number with an average client size between $1 million and $5 million?
b. What is the probability that at least eight CPA financial advisors have an average client size between $500,000 and $1 million?
c. What is the probability that two, three, or four CPA financial advisors have an average client size between $1 million and $5 million?
d. What is the probability that none of the CPA financial advisors have an average client size between $500,000 and $1 million?
Round the answer to 5 decimal places.What is the probability that none have an average client size between $1 million and $5 million?
(Answers for a. and b. round to 2 decimal places, answers for c. and d. round to 5 decimal places.)
End of Section Problem 5.17
Find the following values by using the Poisson formula.
Appendix A Statistical Tables
(Round intermediate values to 4 decimal places. Round your answers to 4 decimal places.)
a. P(x = 5 | λ = 2.1) =
b. P(x = 2 | λ = 4.3) =
c. P(x ≤ 3 | λ = 4.4) =
d. P(x = 0 | λ = 2.6) =
e. P(x = 1 | λ = 5.6) =
f. P(4 < x < 8 | λ = 4.2) =