(a) What is the minimum UGPA that would still place a student in the top 5% of UGPAS? (b) Between what two values does the middle 50% of the UGPAS lie?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Title: Understanding Undergraduate GPAs Through Normal Distribution**
**Description:**
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.
**Questions:**
(a) What is the minimum UGPA that would still place a student in the top 5% of UGPAs?
(b) Between what two values does the middle 50% of the UGPAs lie?
**Graph Explanation:**
The graph is a normal distribution curve representing the UGPAs. Key details are:
- **Mean (μ):** 3.32
- **Standard Deviation (σ):** 0.21
- **X-axis:** Represents the grade point average.
- The graph shows a symmetrical bell curve centered at a mean UGPA of 3.32.
**Additional Information:**
(a) The minimum UGPA that would still place a student in the top 5% of UGPAs is [box for answer].
**Note to Students:**
Use this information to understand how GPA distributions can influence admissions outcomes and to calculate critical cutoff points using statistical methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4e1d665-36e2-4178-b2da-c041c14f10da%2Fea993f42-4e9c-483d-8df4-95c67f0753b7%2Flmr9hg9_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
