Could someone please check my answer.

#1
High school students who take the SAT mathematics exam a second time generally score higher than on their first try. The change in score has a normal distribution with standard deviation 40. A random sample of 1500 gains an average of 25 points on their second try.

A. Give the 90%,95%,and 99% confidence intervals for u

B. What are the margins of error for 90%, 95%, and 99% confidence? How does increasing the confidence level affect the margin of error of a confidence interval.

C. Suppose that the same result had come from a sample of 500 students. Give the 95% confidence interval for the population mean u in this case.

D. Then suppose that a sample of 5000 students had produced the sample mean 25 again give the 95 % confidence interval for u

E. What are the margins of error for the sample sizes 500, 1500 and 5000 for a 95% confidence interval? How does increasing the sample size affect the margin of error of a confidence interval?


Here's my answers

A. 90%= 23.31 to 26.69, 95%= 22.98 to 27.02 and 99%= 22.35 to 27.65

B. 90%= 1.69, 95%= 2.02, 99%=2.65 It also increases.

C. 21.49 to 28.51

D. 23.88 to 26.12

E. 500- 3.51
1500- 2.02
5000- 1.12 It decreases the margin of error.