Question

normal distribution: area between two points
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a set of elementary school student heights are normally distributed with a mean of 105 centimeters and a standard deviation of 7 centimeters.
what proportion of student heights are between 94.5 centimeters and 115.5 centimeters?
you may round your answer to four decimal places.

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set.
For $x = 94.5$, $z_1=\frac{94.5 - 105}{7}=\frac{- 10.5}{7}=-1.5$.
For $x = 115.5$, $z_2=\frac{115.5 - 105}{7}=\frac{10.5}{7}=1.5$.

Step2: Use the standard normal distribution table

We want to find $P(-1.5From the standard - normal distribution table, $P(Z < 1.5)=0.9332$ and $P(Z<-1.5)=0.0668$.
So $P(-1.5

Answer:

$0.8664$