Question

In a survey of women in a certain country​ (ages 20−​29), the mean height was 65.1 inches with a standard deviation of 2.91 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

a) P(X < x) = 0.95

Or, P((X - )/ < (x - )/) = 0.95

Or, P(Z < (x - 65.1)/2.91) = 0.95

Or, (x - 65.1)/2.91 = 1.645

Or, x = 1.645 * 2.91 + 65.1

Or, x = 69.89

The height which represents the 95th percentile is 69.89

b) P(X < x) = 0.25

Or, P((X - )/ < (x - )/) = 0.25

Or, P(Z < (x - 65.1)/2.91) = 0.25

Or, (x - 65.1)/2.91 = -0.67

Or, x = -0.67 * 2.91 + 65.1

Or, x = 63.15

The height which represents the first quartile is 63.15.