Question

The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?

Answer 1

Answer:

95% of students are between 14 and 18 years old

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

$\mu=16$

The standard deviation is:

$\sigma=1$

The z-score formula is:

$Z = \frac{x-\mu}{\sigma}$

For x=14 the Z-score is:

$Z_{14}=\frac{14-16}{1}=-2$

For x=18 the Z-score is:

$Z_{18}=\frac{18-16}{1}=2$

Then we look for the percentage of the data that is between $-2$ deviations from the mean.

According to the empirical rule 95% of the data is less than 2 standard deviations of the mean.  This means that 95% of students are between 14 and 18 years old