   Chapter 8.4, Problem 47E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# College standards At a certain college, CPAs are normally distributed with a mean GPA of 2.48 and a standard deviation of 0.9. If the college wants to limit the number of academic suspensions to at most 15% of its students, find the academic suspension threshold GPA so that at most 15% of students fall below this GPA.

To determine

To calculate: The academic suspension threshold GPA so that at most 15% of students fall below this GPA if at a certain college, GPAs are normally distributed with a mean GPA of 2.48 and a standard deviation of 0.9. If the college wants to limit the number of academic suspensions to at most 15% of its students.

Explanation

Given Information:

At a certain college, GPAs are normally distributed with a mean GPA of 2.48 and a standard deviation of 0.9. If the college wants to limit the number of academic suspensions to at most 15% of its students.

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

Calculation:

Consider the GPA as x.

Here it is normally distributed and the mean and standard deviation are as follows,

μ=2.48σ=0.9

Now the college wants to limit the number of academic suspensions to at most 15% of its students, to find the academic suspension threshold GPA so that at most 15% of students fall below this GPA

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