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Chapter 10: Q. AP3.20 (page 703)

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top10%of the class will receive an A, the next20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum grade a student could attain and still receive an F for the course?

a.70b.69.27c.65.75d.62.84e.57

Short Answer

Expert verified

The correct option is:

c.65.75is the approximate maximum grade a student could attain and still receive an F for the course.

Step by step solution

01

 Step 1: Given information 

We have to tell about the approximate maximum grade a student could attain and still receive an F for the course.

02

Explanation 

While much information is provided, the inquiry solely concerns the value at which a student will receive an F. (but anything more will be a D). The problem further specifies that anything less than 10%will result in an F.

For a mean of 76and a standard deviation of 1, we don't have a normal distribution table. The trick is to convert to X using the Z score form after using the standardised normal table.

Then usez0=x0-渭蟽

Multiply by 8and add 76to get the answer.

x0=-1.28*8+76鈮�65.75

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