Question

In a survey of women in a certain country​ (ages 20−​29) the mean height was 64.2 inches with a standard deviation of

2.93 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 = = 64.2 inches

standard deviation = = 2.93 inches

a ) The 95th ​percentile

Using standard normal table,

P(Z < z) = 95%

P(Z < z) = 0.95

P(Z < 1.645) = 0.95

z = 1.65

Using z-score formula,

X = z * +

X = 1.65 * 2.93 + 64.2

= 69.0345

The 95th ​percentile = 69.03

b ) The first​ quartile Q₁

P(Z < z) = 25%

P(Z < z) = 0.25

P(Z < -0.6745) = 0.25

z = -0.68

Using z-score formula,

X = z * +

X = - 0.68 * 2.93 + 64.2

= 62.2076

The first​ quartile Q₁ = 62.21