Answer to Question #321402 in Statistics and Probability for Sixie

Question

A population of size N=150 has u=8 and standard deviation of o=5.4. What is the probability that a random sample of size n=20 will have a mean of 9.5 above.

Answer 1

Given,

Mean of population $\mu=8$

Standard deviation $\sigma = 5.4$

Using

$P(\bar X >9.5)= \dfrac{\bar X-\mu}{\frac{\sigma}{\sqrt n}}$

$P( \bar X>9.5)= \dfrac{9.5-8}{\frac{5.4}{\sqrt{20}}}=\dfrac{1.5}{1.20}=1.25$

So, $P(Z>1.25)=0.1056$