Use the empirical rule to solve the problem. 6) At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6?
Use the empirical rule to solve the problem. 6) At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:**Using the Empirical Rule to Solve the Problem**
6) At one college, GPAs are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6?
### Explanation:
The empirical rule, also known as the 68-95-99.7 rule, is used to estimate the percentage of values that lie within a certain number of standard deviations from the mean in a normal distribution.
- **Mean (μ):** 3
- **Standard Deviation (σ):** 0.6
**Step 1: Calculate the Intervals**
- **1 Standard Deviation (±1σ):**
- Lower bound: μ - σ = 3 - 0.6 = 2.4
- Upper bound: μ + σ = 3 + 0.6 = 3.6
**Step 2: Determine the Percentage**
According to the empirical rule:
- Approximately 68% of the data falls within ±1 standard deviation from the mean.
**Conclusion:**
Thus, approximately 68% of students have a GPA between 2.4 and 3.6.
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