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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**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.
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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