28. Assigning Grades Professor Morgan uses a normal distribu- tion to assign gra

Question

28. Assigning Grades Professor Morgan uses a normal distribu- tion to assign grades in his Finite Mathematics class. He assigns an A to students scoring more than 2 standard deviations above the mean and an F to students scoring more than two standard deviations below the mean. He assigns a B to students who score between 1.2 and 2 stan'dard deviations above the mean and a D to students who score between 1.6 and 2 standard deviations below the mean. All other students get a C. What percent of the class receives each grade assuming the scores are normally distributed?

Explanation / Answer

Ans:

For A grade:

2 standard deviations above the mean means that z=2,So,

P(z>2)=0.0228

2.28% gets A grade

For F grade:

2 standard deviations below the mean means that z=-2,So,

P(z<-2)=0.0228

2.28% gets F grade

For B grade

P(1.2<z<2)=P(z<2)-P(z<1.2)

=0.9772-0.8849=0.0923

9.23% gets B grade

For D-grade:

P(-2<z<-1.6)=P(z<-1.6)-P(z<-2)

=0.0548-0.0228=0.0320

3.20% gets D grade

C grade:

P(C grade)=1-0.0228-0.0228-0.0923-0.0320=0.8301

83.01% gets C grade

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