Answer to Question #38781 in Statistics and Probability for yancey

Question

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 \sigma= 50. A random sample of 1000 students gains an average of \bar{x}= 22 points on their second try. What is the margin of error for a 95% confidence interval for the mean score gain \mu in the population of all students?