Answer to Question #317375 in Statistics and Probability for cosette

Question

The mean weight of 20-year-old females is 126 pounds and the standard deviation is 15.7. If a sample of 25 females is selected, find the probability that the mean of the sample will be greater than 128.3 pounds. Assume that the variable is normally distributed.

Answer 1

We have a normal distribution, $\mu=126, \sigma=15.7, n=25.$

Let's convert it to the standard normal distribution,

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

$=\cfrac{128.3-126}{15.7/\sqrt{25}}=0.73,$

$P(\bar{X}>128.3)=1-P(\bar{X}<128.3)=\\ =1-P(Z<0.73)=$

$=1-0.7673=0.2327.$ ​(from z-table)