The yield of a chemical process is being studied. from previous experience, yield is known to be normally distributed and the past five days of plant operation have resulted in the following yields 91.6, 88.75, 90.8, 89.62, and 91.2. find a 95% two-sided confidence interval on the true mean yield. (a) calculate the sample mean. round your answer to 2 decimal places.

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?