Answer to Question #345935 in Statistics and Probability for Joe

Question

activity 2 solve the following problems. show all your works. 1 in a study of the life expectancy of 500 people in a certain geographic region, the mean age at death was 720 years, and the standard deviation was 5.3 years. if a sample of 50 people from this region is selected, find the probability that the mean life expectancy will be less than 70 years.

Answer 1

Given $\mu=72.0$ years, $\sigma=5.3$ years, $N=500, n=50.$

$$\sigma_{X}=\dfrac{\sigma}{\sqrt{n}}\sqrt{\dfrac{N-n}{N-1}}=\dfrac{5.3}{\sqrt{50}}\sqrt{\dfrac{500-50}{500-1}}\approx0.7118$$

$$P(X<70)=P(Z<\dfrac{70-72}{0.7118})$$

$$\approx P(Z<-2.80985)\approx0.0025$$