The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places. a) What is the probability that more than three aircraft arrive within an hour? b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.21.

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?