Searches at Switzerland's 406 commercial banks turned up only $3.3 million in accounts belonging to Zaire's deposed president, Mobutu Sese Seko. The Swiss banks had been asked to look a little harder after finding nothing at all the first time round.

a. If President Mobutu's money was distributed in all 406 banks, how much was found, on average, per bank?

b. If a random sample of 16 banks was first selected in a preliminary effort to estimate how much money was in all banks, then assuming that amounts were normally distributed with standard deviation of $2,000, what was the probability that the mean of this sample would have been less than $7,000?