Question

QUESTION 1 A population has a mean of 60 and a standard deviation of 14. Samples of size 64 are randomly selected. Calculate the standard deviation of the sample distribution of X. Round off to 3 decimal places.

Answer 1

Let , , n=64

X + Nu = 60,0 = 14)

Therefore , the distribution of sample mean is , $\bar{X}\to N(\mu_{\bar{X}}=\mu,\sigma_{\bar{X}}=\frac{\sigma}{\sqrt{n}})$

Therefore , the standard deviation of the sample distribution of is ,

X

$\sigma_{\bar{X}}=\frac{\sigma}{\sqrt{n}}=\frac{14}{\sqrt{64}}=1.750$