Question

A population has an average u=50 and standard deviation of ó=2.3.what is the probability that a random sample is size n=8 will have a mean between 52 and 54?

Answer 1

Solution:

$\mu=50,\sigma=2.3,n=8$

$P(52\le X\le 54)=P(X\le 54)-P(X\le 52) \\=P(z\le \dfrac{54-50}{2.3/\sqrt{8}})-P(z\le \dfrac{52-50}{2.3/\sqrt{8}})$

$=P(z\le 4.91)-P(z\le 2.459) =1-0.9931=0.0069$