Question

The life expectancy in the United States is 75 with a standard deviation of 7 years. A random sample of 49 individuals is selected. Round all probabilities to four decimal places.

What is the probability that the sample mean will be larger than 77 years? Answer

What is the probability that the sample mean will be within 1 year of the population mean?

What is the probability that the sample mean will be within 2.5 years of the population mean?

Answer 1

Note that sample mean X follows a Normal distribution with Mean-μ 75 Standard deviation = σ/Vn-1 Note that z-(-H)/(o/Vn) - (x-75)/1 (Eq.1) follows standard Normal. when x = 77, from (Eq.1) , z-2 P 77)-P(Z> 2)-1-P(Z 2)-1-0.9772-0.0228 (ans) When R 74, from (Eq.1),z -1 When X-76, from (Eq.1),z 1 P(74 < X < 76-PC1 < z <1)-P(Z < 1) . P(Z <-1-0.84 13-0.1587 = 0.6826 When x = 72.5, from (Eq.1), z =-2.5 (ans) When x 77.5, from (Eq.1),z 2.5 P(72.5X 77.5)-P(-2.5 Z2.5)- P(Z2.5) - P(Z-2.5)-0.9938-0.0062-0.9876 (ans)