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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 rule, approximately what percent of the students are between 14 and 18 years old?

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Answer:

95% of students are between 14 and 18 years old

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 = (x-\mu)/(\sigma)

For x=14 the Z-score is:


Z_(14)=(14-16)/(1)=-2

For x=18 the Z-score is:


Z_(18)=(18-16)/(1)=2

Then we look for the percentage of the data that is between
-2 <Z <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

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