The grading system known as \"grading on the curve\" is based on the assumption

Question

The grading system known as "grading on the curve" is based on the assumption that grades are often distributed according to the normal curve and that a certain percent of a class should receive each grade, regardless of the performance of the class as a whole. The following is how one professor might grade on the curve. What percent of the students receive a C? Approximately % of the students in this course will receive a C. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation / Answer

3/4=0.75

mean-0.75

and mean+0.75

To find the probability of P (0.75<Z<0.75), we use the following formula:

P (0.75<Z<0.75 )=P ( Z<0.75 )P (Z<0.75 )

Step 3: P ( Z<0.75 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<0.75 )=0.7734.

Step 4: P ( Z<0.75 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=0.75 we have:

P ( Z<0.75)=1P ( Z<0.75 )

P ( Z<0.75 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<0.75 )=0.7734 so,

P ( Z<0.75)=1P ( Z<0.75 )=10.7734=0.2266

At the end we have:

P (0.75<Z<0.75 )=0.5468

0.5468=54.68%

ANSWER 54.68%

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