Question

normal distribution: area above or below a point
you might need: calculator
a set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. uma is a middle school student with a height of 165 centimeters.
what proportion of student heights are higher than umas 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 $x = 165$ (Uma's height), $\mu=150$ (mean), and $\sigma = 20$ (standard deviation).
$z=\frac{165 - 150}{20}=\frac{15}{20}=0.75$

Step2: Find the area to the right of the z - score

We know that the total area under the normal - distribution curve is 1. The area to the left of $z = 0.75$ can be found using a standard normal distribution table or a calculator with a normal - distribution function. Using a calculator (e.g., TI - 84 Plus: normalcdf(-1000,0.75)), the area to the left of $z = 0.75$ is approximately $0.7734$. The area to the right of $z = 0.75$ (the proportion of student heights higher than Uma's) is $1-0.7734 = 0.2266$.

Answer:

$0.2266$