Answer to Question #320160 in Statistics and Probability for Faye

Question

1. The scores of the individual students on a national test have a normal

distribution with the mean 19.5 and standard deviation of 5.6. At Ramos High

School, 86 students took the test. If the scores at this school have the same

distribution as national scores, what are the mean and standard deviation of the

sample mean for 86 students?

Answer 1

$\mu$ =19.5

$\sigma$ =5.6

n=86

According to the central limit theorem

sample mean =$\mu$

sample standard deviation =$\sigma/\sqrt(n )$

Thus the sample mean =19.5

sample standard deviation =$5.6/sqrt(86)$

sample standard deviation =0.6039