Question

In a survey of women in a certain country​ (ages 20−​29), the mean height was 64.6 inches with a standard deviation of 2.77 inches. Answer the following questions about the specified normal distribution.

​(a) What height represents the 95th ​percentile?

​(b) What height represents the first​ quartile?

Answer 1

Solution:-

Given that,

mean = = 64.6

standard deviation = = 2.77

a) Using standard normal table,

P(Z < z) = 95%

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95  

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 2.77 + 64.6

x = 69.16

b) Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = - 0.6745

Using z-score formula,

x = z * +

x = - 0.6745 * 2.77 + 64.6

x = 62.73

First quartile =Q1 = 62.73