A random sample of 1000 Indiana high school seniors found a mean of 1072 and a standard deviation of 165 on their SAT score.

a) (2 pts) What is the margin of error for the 95% confidence interval? Use 2 decimals. Show your work.

b) (3 pts) What is the interval (show upper and lower bound of the interval) for the true population mean for all Indiana high school seniors at the 95% confidence level? Use 2 decimals. Show your work.

c) (2 pts) Explain what would happen to the interval if I wanted 99% confidence instead of 95% confidence.