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## 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 ru

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?

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2021-09-11T02:44:16+00:00
2021-09-11T02:44:16+00:00 1 Answer
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## Answers ( )

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:

The standard deviation is:

The z-score formula is:

For x=14 the Z-score is:

For x=18 the Z-score is:

Then we look for the percentage of the data that is between 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