A psychological study found that the mean length of time that boys remained engaged with a science exhibit at a museum was 107 seconds with a standard deviation of 117 seconds. Assume that the 117 seconds represents the population standard deviation. The sample size is 36 and let the confidence level be 95%. (a) Find and interpret the margin of error. (b) How large a sample size is needed to estimate to within 30 seconds with 95% confidence