Question

4. The mean hemoglobin level in the blood for a certain large group of individuals is 21.0 grams per milliliter (g/ml). The standard deviation is 2 g/ml. If a sample of 25 individuals is selected, find the probability that the mean will be greater than 21.3 g/ml. Assume that the variable is normally distributed.

Answer 1

We have a normal distribution, $\mu=21.0, \sigma=2, n=25.$

Let's convert it to the standard normal distribution,

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

$=\cfrac{21.3-21.0}{2/\sqrt{25}}=0.75,$

$P(\bar{X}>21.3)=1-P(\bar{X}<21.3)=\\ =1-P(Z<0.75)=$

$=1-0.7734=0.2266$ ​(from z-table)