The ages of students attending a college employment centre are normally distributed with a mean of 22 and a standard deviation of 1.2. The middle 95% of the students are approximately between what ages? (Use Empirical Rule)
Calculate your answer using this Spreadsheet template.

To solve this problem using the Empirical Rule, we can break it down as follows:

The Empirical Rule states that for a normal distribution:
- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations of the mean.
- 99.7% of the data falls within 3 standard deviations of the mean.

We are interested in the middle 95%, which corresponds to the range between ±2 standard deviations from the mean.

Given:
- Mean (\(\mu\)) = 22
- Standard deviation (\(\sigma\)) = 1.2

To calculate the range of ages for the middle 95%:
1. Subtract 2 standard deviations from the mean to find the lower bound:
   \[
   \text{Lower bound} = \mu - 2\sigma = 22 - 2(1.2) = 22 - 2.4 = 19.6
   \]
2. Add 2 standard deviations to the mean to find the upper bound:
   \[
   \text{Upper bound} = \mu + 2\sigma = 22 + 2(1.2) = 22 + 2.4 = 24.4
   \]

Thus, the middle 95% of the students' ages are between 19.6 and 24.4 years old.

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If you'd like to input this into a spreadsheet:
- In one cell (e.g., A1), input the mean (22).
- In another cell (e.g., A2), input the standard deviation (1.2).
- In cell A3, use the formula `=A1-2*A2` for the lower bound.
- In cell A4, use the formula `=A1+2*A2` for the upper bound.

Would you like more details on this calculation or help with the spreadsheet?

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### Related Questions:
1. What percentage of students fall between 21 and 23 years old?
2. How many standard deviations from the mean would include 99% of students' ages?
3. If the mean age changes to 23, what would the new middle 95% age range be?
4. How does the Empirical Rule apply to skewed distributions?
5. Can the Empirical Rule be used for any distribution that is not normal?

### Tip:
The Empirical Rule is most accurate for distributions that are perfectly normal. Always check the shape of your data distribution before applying it!

The ages of students attending a college employment centre are normally distributed with a mean of 22 and a standard deviation of 1.2. The middle 95% of the students are approximately between what ages? (Use Empirical Rule) Calculate your answer using this Spreadsheet template.

This guide explains how to use the Empirical Rule to calculate the middle 95% of student ages, assuming a normal distribution with a mean of 22 and a standard deviation of 1.2. It includes step-by-step calculations for both the lower and upper bounds, suitable for high school students.

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