Question

Heights for group of people normally distributed with mean = 63 inches and standard deviation = 2.9 inches. Find the height, h such that about 20% of people in the group are shorter than that height. (Round the answer to the nearest tenth.)

h = in.

What is the percentile, p ranking for that height?

p = %

Answer 1

Solution:

Given: Heights for group of people normally distributed with mean = 63 inches and standard deviation = 2.9 inches.

We have to find the height, h such that about 20% of people in the group are shorter than that height.

that is:

P( X < h) =0.20

Thus find z value such that:

P( Z < z) =0.20

Look in z  table for Area = 0.2000 or its closest area and find corresponding z value.

Area 0.2005 is closest to 0.2000 and it corresponds to -0.8 and 0.04

that is  z = -0.84

Now use following formula to find x value:

that is:

What is the percentile, p ranking for that height?

Since  20% of people in the group are shorter than that height,

thus p = 20%