1) A class has 80 students. Test 2 had a class average of 78 and a variance of 4

Question

1) A class has 80 students. Test 2 had a class average of 78 and a variance of 49. Answer the following 7 questions. (Assume Normal distribution). Assume a 90-80-70-60 = A-B-C-D scale.

1. What is the probability of getting an A?
2. How many will get an A?
3. What is the probability of getting a B?
4. What is the probability of getting a C?
5. How many people will fail the class?
6. If the bottom 5% will get an F, what will be the cut-off score?
7. If the top 15% get an A, what is the cutoff score for an A?

Answer choices:

0.408
85.28
.3440
66.485
0.0436
3.488
.4830

Explanation / Answer

Mean =78     sd =sqrt(49)=7

Z for 90, z=(90-78)/7 =1.71

P( x >90) =P(z >1.71) = 0.0436

2. How many will get an A?

0.0436*80= 3.488

3. What is the probability of getting a B?

Z for 80, z=(80-78)/7 =0.29

P( 80<x<90) =P(0.29<z<1.71)

= 0.3859- 0.0436

=0.3423

Answer : 0.344

4. What is the probability of getting a C?

Z for 70, z=(70-78)/7 =-1.14

P( 70<x<70) =P(-1.14<z<0.29)

= 0.8729 - 0.3859 =0.487

Answer: 0.483

5. How many people will fail the class?

Z for 60, z=(60-78)/7 =-2.57

P( x ,60) = P( z <-2.57) =0.0051

people fail =0.0051*80=0.408
6. If the bottom 5% will get an F, what will be the cut-off score?

Z value for bottom 5% = -1.645

X=78-1.645*7 = 66.485

7. If the top 15% get an A, what is the cutoff score for an A?

Z value for bottom 15% = 1.036

X=78+1.04*7 = 85.28

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