Question

A set of middle school student heights are normally distributed with a mean of 150150150 centimeters and a standard deviation of 202020 centimeters. Darnell is a middle school student with a height of 161.4161.4161, point, 4 centimeters.

Answer 1

Complete question :

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnell is a middle school student with a height of 161.4 centimeters.

What proportion of student heights are lower than Darnell's height?

Answer:

0.716 (71.6%)

Step-by-step explanation:

Given that :

Mean, μ = 150

Standard deviation, σ = 20

Darnell's height, x = 161.4

(x < 161.4)

We obtain the standardized score, then find the proportion using a standard normal distribution ;

Zscore = (x - μ) / σ

Zscore = (161.4 - 150) / 20

Zscore = 11.4 / 20

Z = 0.57

P(Z < 0.57) = 0.71566 (Z probability calculator)

This means that about 0.716 (0.716 * 100% = 71.6%) of student's height are lower than 161.4 centimeters