**Educational Material: Understanding UGPA Distribution** The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be modeled using a normal distribution, as illustrated in the accompanying figure. ### Statistical Questions: 1. **Minimum UGPA for Top 5% Placement:** - What is the minimum UGPA needed to position a student within the top 5% of UGPAs? 2. **UGPA Range for Middle 50%:** - 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 5% of UGPAs is \[\_\_\_\_\]. - **(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.)** ### Graphical Representation: - **Normal Distribution Diagram:** - The graph showcases a bell-shaped curve typical of normal distribution, with a peak indicating the mean UGPA. - The horizontal axis represents the Grade Point Average (GPA). - Notable points marked on the curve include: - \( p = 3.38 \) - \( \sigma = 0.13 \) This representation helps visualize how UGPAs are distributed among students, providing insight into percentile rankings and variability in student performance.

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**Educational Material: Understanding UGPA Distribution**

The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be modeled using a normal distribution, as illustrated in the accompanying figure.

### Statistical Questions:

1. **Minimum UGPA for Top 5% Placement:**
   - What is the minimum UGPA needed to position a student within the top 5% of UGPAs?

2. **UGPA Range for Middle 50%:**
   - 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 5% of UGPAs is \[\_\_\_\_\].
  - **(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.)**

### Graphical Representation:

- **Normal Distribution Diagram:**
  - The graph showcases a bell-shaped curve typical of normal distribution, with a peak indicating the mean UGPA.
  - The horizontal axis represents the Grade Point Average (GPA).
  - Notable points marked on the curve include:
    - \( p = 3.38 \)
    - \( \sigma = 0.13 \)

This representation helps visualize how UGPAs are distributed among students, providing insight into percentile rankings and variability in student performance.
Transcribed Image Text:**Educational Material: Understanding UGPA Distribution** The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be modeled using a normal distribution, as illustrated in the accompanying figure. ### Statistical Questions: 1. **Minimum UGPA for Top 5% Placement:** - What is the minimum UGPA needed to position a student within the top 5% of UGPAs? 2. **UGPA Range for Middle 50%:** - 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 5% of UGPAs is \[\_\_\_\_\]. - **(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.)** ### Graphical Representation: - **Normal Distribution Diagram:** - The graph showcases a bell-shaped curve typical of normal distribution, with a peak indicating the mean UGPA. - The horizontal axis represents the Grade Point Average (GPA). - Notable points marked on the curve include: - \( p = 3.38 \) - \( \sigma = 0.13 \) This representation helps visualize how UGPAs are distributed among students, providing insight into percentile rankings and variability in student performance.
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