Answer to Question #328077 in Statistics and Probability for robot

Question #328077

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?


1
Expert's answer
2022-04-15T10:29:14-0400

a. P(65<X<69)=P(65662.5<Z<69662.5)=P(0.4<Z<1.2)=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.=P(Z<1.2)-P(Z<-0.4)=0.5404.


b. P(X>72)=P(Z>72662.5)=P(Z>2.4)=1P(Z<2.4)=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.


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