Answer to Question #173280 in Statistics and Probability for Denisse Bisuña

Question

the scores of individual students on a national test have a normal distribution with mean of 18.6 and standard deviation of 5.9. At Federico Ramos Rural High School, 76 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 76 students?

Answer 1

μ = 18.6

σ = 5.9

n = 76

Mean of sample for 76 students

$E(\bar{x}) = μ = 18.6 \\ σ(\bar{x}) = \frac{σ}{\sqrt{n}}= \frac{5.9}{\sqrt{76}} = 0.6767$

Mean of sample mean of 76 students is 18.6

Standard deviation of sample mean of 76 students is 0.6767