Answer to Question #311893 in Statistics and Probability for opalyn

Question

The weights of male students are normally distributed with a mean of 150 lbs. and a standard deviation of 25 lbs. What is the probability that 25 randomly selected make students will have a mean weight of more than 155 lbs?

Answer 1

We have a normal distribution, $\mu=150, \sigma=25, n=25.$

Let's convert it to the standard normal distribution,

$z=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}$ =

$=\cfrac{155-150}{25/\sqrt{25}}=1,$

$P(\bar{X}>155)=1-P(\bar{X}<155)=1-P(Z<1)=$

$=1-0.8413=0.1587$ ​(from z-table)