Answer to Question #189608 in Statistics and Probability for Aditya Sharma

Question

The scores of individual students on a national achievement test have a normal distribution with a mean of 20.8 and a standard deviation of 1.9 at Feliciano delos Santos high school, 84 students took the test.if the scores of the students at this school have the same distribution as the national scores, how will you describe the sampling distribution of the scores of these students?assume that the population is infinite. Use the given steps above

Answer 1

$\mu=20.8,\sigma=1.9, n=84$

Using central limit theorem-

$\bar{X}$ ~$~N(\mu,\dfrac{\sigma}{\sqrt{n}})$

So mean of sampling distribution $\bar{x}=\mu=20.8$

Standard deviation of samples $s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.9}{\sqrt{84}}=0.2073$