Question

In a survey of women in a certain country​

the mean height was

65.9

inches with a standard deviation of

2.72inches. Answer the following questions about the specified normal distribution.

​(a) What height represents the

85th

​percentile?

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

Answer 1

For normal distribution, P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 65.9 inches

Standard deviation = 2.72 inches

a) Let E represent the 85th percentile

P(X < E) = 0.85

P(Z < (E - 65.9)/2.72) = 0.85

Take Z value corresponding to probability of 0.8500 from standard normal distribution table.

(E - 65.9)/2.72 = 1.04

E = 68.73 inches

68.73 inches represents the 85th percentile.

b) Let Q represent the first quartile

P(X < E) = 0.25

P(Z < (Q - 65.9)/2.72) = 0.25

Take Z value corresponding to probability of 0.2500 from standard normal distribution table.

(Q - 65.9)/2.72 = -0.67

Q = 64.08 inches

64.08 inches represents the first quartile.