Question

a set of elementary school student heights are normally distributed with a mean of 105 centimeters and a standard deviation of 10 centimeters. ikue is an elementary school student with a height of 90.4 centimeters. what proportion of student heights are lower than ikues 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 $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $x = 90.4$, $\mu=105$, and $\sigma = 10$.
$z=\frac{90.4 - 105}{10}=\frac{- 14.6}{10}=-1.46$

Step2: Find the proportion using the standard normal distribution table

We want to find $P(X<90.4)$, which is equivalent to $P(Z < - 1.46)$ using the standard normal distribution. Looking up the value of $P(Z < - 1.46)$ in the standard - normal table (or using a calculator with a normal - distribution function), we get the proportion.
From the standard normal table, $P(Z < - 1.46)=0.0721$

Answer:

$0.0721$