The cost of health care is the subject of many studies that use statistical methods. One such study estimated that the average length of service for home health care among people over the age of 65 who use this type of service is 96.0 days with a standard error of 5.1 days. Assuming that the degrees of freedom are large, calculate a 90% confidence interval for the true mean length of service.

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?