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Chapter 10: Q. 20 (page 669)

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

(a) 70

(b)69.27

(c) 65.75

(d) 62.84

(e)57

Short Answer

Expert verified

The maximum average a student could attain and still receive an F for the course is 65.75i.e., option (c).

Step by step solution

01

Given Information

We are given that the mean is 渭=76and standard deviation is 蟽=8and we are also given that anything below 10%is considered as an F.

We have to find out the maximum average a student can attain and still receive an F for the course.

02

Explanation

Now using Z score formula as the normal distribution table of mean and standard deviation is not given,

P(Z鈮�z0)=0.10and then

we will use z0=x0-渭蟽let this be equation 1....

03

Simplify

Now see the standard table and find the value of Zthat will correspond to 10%.

which gives z0=-1.28

Now put the value in equation 1...

we get -1.28=x0-768

which results x0=65.75

Hence, the maximum average a student could attain is65.75.

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