Answer to Question #333078 in Statistics and Probability for Luffytaro17

Question

In a study of the life expectancy of 450people in a certain geographic region, the mean age of death was 75 years, and the standard deviation was 5.4 years. If a sample of 45 people from this region is selected, what is the probability that the mean life expectancy will be less than 69

years

Answer 1

We have a normal distribution, $μ=75,σ=5.4,n=45.$

Let's convert it to the standard normal distribution,

$\bar{z}=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\cfrac{69-75}{5.4/\sqrt{45}}=-7.45,\\ P(\bar{X}<69)=P(\bar{Z}<-7.45)=\\ =0\text{ (from z-table).}$