Question

a set of elementary school student heights are normally distributed with a mean of 105 centimeters and a standard deviation of 10 centimeters. faisal is an elementary school student with a height of 103.1 centimeters. what proportion of student heights are lower than faisals height? you may round your answer to four decimal places.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 103.1$ (Faisal's height), $\mu = 105$ (mean), and $\sigma = 10$ (standard deviation).
$z=\frac{103.1 - 105}{10}=\frac{-1.9}{10}=- 0.19$

Step2: Find the proportion

We use the standard normal distribution table (or z - table) to find the proportion of values to the left of $z=-0.19$. Looking up $z = - 0.19$ in the z - table, we get the value $0.4247$.

Answer:

$0.4247$