SAT scores are normally distributed with a mean and standard deviation

Question

SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 90% confidence interval to 15 points, how many students should the administrator sample?

Answer 1

Hi Emma,

Formula for this sample size calculation is:

n = (z*sigma/m)²

z*= z-critical value

sigma = standard deviation

m= margin of error

z-critical value for 95% confidence is worth memorizing; it is:

z* = 1.645

Thus:

z* = 1.645

sigma = 300

m = 15

n = [(1.645*300)/15]²

n= 1082.41, but sample sizes must always be rounded up, so:

n = 1083

I hope this helps.