MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The image discusses the undergraduate grade point averages (UGPA) of students taking an admissions test, which follow a normal distribution. This distribution is represented by a graph with a mean (μ) of 3.24 and a standard deviation (σ) of 0.21.

### Questions:
(a) What is the minimum UGPA that would still place a student in the top 10% of UGPAs?  
(b) Between what two values does the middle 50% of the UGPAs lie?

### Answers:
(a) The minimum UGPA that would still place a student in the top 10% of UGPAs is **3.51**. (Rounded to two decimal places.)

(b) The middle 50% of UGPAs lies between **3.10** on the low end and **3.38** on the high end. (Rounded to two decimal places.)

### Graph Explanation:
The graph is a normal distribution curve representing the UGPAs. The horizontal axis is labeled "Grade point average" and ranges from approximately 2.48 to 4. The vertical line at the mean (μ = 3.24) marks the center of the distribution, and the spread of the curve indicates variability, defined by the standard deviation (σ = 0.21). The shaded areas under the curve correspond to specific percentile regions as referenced in the questions.
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Transcribed Image Text:The image discusses the undergraduate grade point averages (UGPA) of students taking an admissions test, which follow a normal distribution. This distribution is represented by a graph with a mean (μ) of 3.24 and a standard deviation (σ) of 0.21. ### Questions: (a) What is the minimum UGPA that would still place a student in the top 10% of UGPAs? (b) Between what two values does the middle 50% of the UGPAs lie? ### Answers: (a) The minimum UGPA that would still place a student in the top 10% of UGPAs is **3.51**. (Rounded to two decimal places.) (b) The middle 50% of UGPAs lies between **3.10** on the low end and **3.38** on the high end. (Rounded to two decimal places.) ### Graph Explanation: The graph is a normal distribution curve representing the UGPAs. The horizontal axis is labeled "Grade point average" and ranges from approximately 2.48 to 4. The vertical line at the mean (μ = 3.24) marks the center of the distribution, and the spread of the curve indicates variability, defined by the standard deviation (σ = 0.21). The shaded areas under the curve correspond to specific percentile regions as referenced in the questions.
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