A key metric in the cell phone industry is average revenue per user (ARPU) which represents the average dollar amount that a customer spends per store visit. Recently, AT&T reported their ARPU was $67.81. Suppose the standard deviation for this population is $18.45. What is the probability that the ARPU will be between $62 and $66 from a random sample of 35 customers?

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?