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.

The Empirical Rule (or 68-95-99.7 Rule) states that for a normally distributed dataset:

- 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.

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

To find the range covering the middle 95% of the ages, we need to go 2 standard deviations on either side of the mean.

### Calculation:
Lower bound: \( \mu - 2\sigma = 22 - 2(1.2) = 22 - 2.4 = 19.6 \)  
Upper bound: \( \mu + 2\sigma = 22 + 2(1.2) = 22 + 2.4 = 24.4 \)

Thus, the middle 95% of the students are approximately between the ages of 19.6 and 24.4.

Would you like to see more details or ask any further questions?

---

Here are 5 related questions:
1. What percentage of students fall between 1 and 3 standard deviations from the mean?
2. How do the boundaries change if the standard deviation increases to 2?
3. How would the age distribution change if the mean were increased to 25?
4. What ages encompass the middle 68% of the students?
5. Can we use the Empirical Rule for distributions that are not normal?

**Tip:** The Empirical Rule is only applicable to normally distributed data; if the data is skewed, different rules apply.

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)

Learn how to apply the Empirical Rule to find the range covering the middle 95% of ages in a normal distribution with a mean of 22 and standard deviation of 1.2. This problem uses statistical concepts like the Empirical Rule (68-95-99.7 Rule) and standard deviations. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation