Answer to Question #328077 in Statistics and Probability for robot

Question

JGU students recently conducted a study to record the height of Asian Females in Haryana. They found the heights to be normally distributed with a mean 66 inches and a standard deviation of 2.5 inches.

a. Suppose a female is randomly selected. What is the probability of her height being between 65 and 69 inches.

b. Is it possible to meet a female in Haryana with a height more than 72 inches?

Answer 1

a. $P(65<X<69)=P(\frac{65-66}{2.5}<Z<\frac{69-66}{2.5})=P(-0.4<Z<1.2)=$

$=P(Z<1.2)-P(Z<-0.4)=0.5404.$

b. $P(X>72)=P(Z>\frac{72-66}{2.5})=P(Z>2.4)=1-P(Z<2.4)=$0.0082.

This case is not impossible but very uncommon.