Question

Sat scores are distributed with a mean of 1,500 and a standard deviation of 300. you are interested in estimating the average sat score of first year students at your college. if you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

Answer 1

The z-score is given by:
z=(x-mean)/s.d
the z-score giving us P(0.95)=1.96 and -1.96
thus;
-1.96=(x-1500)/300
-588=x-1500
x=-588+1500
x=912
also:
1.96=(x-1500)/300
588=x-1500
x=588+1500
x=2,088
therefore the sample size of the student picked will be given by:
2,088-912
=1,176