End of Section Problem 5.14 Your answer is partially correct. Try again. Studies

Question

End of Section Problem 5.14 Your answer is partially correct. Try again. 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 obs cash out their 401(k) plans f 16 workers who have recently changed Obs that had 401 k ians 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 0.105 0.0880 cashed out? Click if you would like to Show Work for this question:

Explanation / Answer

Solution:

a) n = 16, p = 0.5
P[X= x] = 16Cx*(1/2)x *(1/2)n-x = nCx /2n

P[X>10] = (16c11+16c12+.... 16c22)/216 = 0.1051

b) n = 10, p = 0.8
P[X= 6] = 10c6 * 0.56 * 0.54 = 0.2050

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