One hundred sixty-five of the 225 high school students surveyed at a local school say they went outside more during school hours as elementary school students than they do now as high school students. calculate the margin of error (me), rounded to the nearest tenth of a percent. is it reasonable that the state education department claims the percentage for the entire state is 78%? justify your answer.

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?