Police recorded the average speed of cars driving on a busy street by a school. For a sample of 36 speeds, it was determined that the average amount over the speed limit for the 36 speeds was 12.2 mph with a standard deviation of 7 mph. The 95% confidence interval estimate for this sample is 9.83 mph to 14.57 mph.

a) What is the margin of error for this problem?

b) What size sample is needed to reduce the margin of error to no more than 1?

Please show all work. It would be very helpful for me to learn.