The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (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? p324 a-021 248 324 Grade point average (a) The minimum UGPA that would still place a student in the top 10% of UGPAS is 3.51 (Round to two decimal places as needed.) (b) The middle 50% of UGPAS lies between on the low end and on the high end. (Round to two decimal places as needed.)
The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (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? p324 a-021 248 324 Grade point average (a) The minimum UGPA that would still place a student in the top 10% of UGPAS is 3.51 (Round to two decimal places as needed.) (b) The middle 50% of UGPAS lies between on the low end and on the high end. (Round to two decimal places as needed.)
MATLAB: An Introduction with Applications
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78ce8110-2855-463d-9dee-4955d084eeee%2F3d8c6478-bc18-412e-a42c-6fa2a7f36a18%2F15wyis8_processed.jpeg&w=3840&q=75)
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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