Question

Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. P9, the 9th percentile is the bone density score separating the bottom 9% from the top 91%. What is the bone density score corresponding to P9?

Answer 1

Solution:

We are given that : Bone density test scores are normally distributed with a mean of 0 and

a standard deviation of 1.

we have to find 9th percentile with graph.

Since mean is 0 and standard deviation is 1 , we can assume Standard normal distribution.

Thus

P( Z < z value ) = 9%

P( Z < z value ) = 0.0900

Look in z table for area = 0.0900 or its closest area and find corresponding z value.

From above z table , we can see area 0.0901 is closest to -1.3 and 0.04

Thus z value is = -1.34

Thus P( Z < -1.34 ) = 0.0901

Thus 9th percentile is -1.34.