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) account less than $5, 000 opt to take their balance in cash rather than roll it over into individual retirement accounts when they change jobs.
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?