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StatisticsEssentials Of StatisticsTo be accepted into an honor society, a student must have a grade-point average (GPA) in the top 10% of the school. If the mean GPA at the school is 2.78 and the standard deviation is 0.33, which of the following GPAs would qualify? 3.20 , 3.21 , 3.25 , 3.30 , 3.35BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 5, Problem 5.12P

Textbook Problem

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To be accepted into an honor society, a student must have a grade-point average (GPA) in the top 10% of the school. If the mean GPA at the school is 2.78 and the standard deviation is 0.33, which of the following GPAs would qualify?

Expert Solution

To determine

**To find:**

The qualified GPA.

**Given:**

The mean GPA is 2.78 and the standard deviation is 0.33.

**Description:**

The normal curve is symmetrical and its mean is equal to the median. The area below and above the mean is 50% or 0.05.

**Formula used:**

Let the data values be denoted by

The formula to calculate the

Where,

**Calculation:**

Given that the mean is 2.78 and standard deviation is 0.33.

For the GPA of 3.20,

Substitute 3.20 for

The area between mean and the score

Use the concept of symmetry, the area below the score

The probability that the GPA is below 3.20 is 0.898.

For the GPA of 3.21,

Substitute 3.21 for

The area between mean and the score

Use the concept of symmetry, the area below the score

The probability that the GPA is below 3.21 is 0.9032.

For the GPA of 3.25,

Substitute 3.25 for

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