Question

1. Suppose the mathematics SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. If a school only accepts students with SAT math scores in the top 10 percent, what are the minimum SAT scores that would be acceptable for that school?

Answer 1

z-value for top 10% area in right tail of normal curve is 1.28

Using central limit theorem,

x = mean + z*sigma

here, mean = 500 and sigma = 100

x = 500 + 1.28*100

x = 628

Hence, minimum acceptable SAT score is 628.