Dear Expert, Can you solve the three questions for me. Thanks! 12. Consider the

Question

Dear Expert, Can you solve the three questions for me. Thanks!

12.

Consider the midterm scores of two chemistry classes. In Class A the mean is 50 and the standard deviation is 10. In Class B the mean is 50 and the standard deviation is 30. Both classes have 100 students in them and both are exactly normally distributed.

Imagine that both professors have decided to give students letter grades according to their z-scores using the following breakdown.

Z-score

Grade

1 or higher

A

0 to 1

B

-1 to 0

C

-2 to -1

D

-2 or lower

F

In Class A, what score would you have to get to receive an A on the midterm?

In Class B, what score would you have to get to receive an A on the midterm?

Explain how you got these answers.

Question 13

Considering the data from the previous question, how many students (out of 100) would you expect to get a score of higher than 20 in Class A? How about Class B? Explain how you you got your answer.

Question 14

Considering the same data, how many students (out of 100) would you expect to get a score higher than 50 in Class A? How about Class B? Explain how you you got your answer.

Z-score

Grade

1 or higher

A

0 to 1

B

-1 to 0

C

-2 to -1

D

-2 or lower

F

Explanation / Answer

Given that mean of class A, .MA=50 anand standard deviation as SA=10

Again for Class B , .MB=50 and standard deviation as SB=30

Hence according to question.

For class A score at Z =1 the score calculated as

X=50 +1*10=60

Hence score 60 or above will get grade A.

For class B score at Z=1 calculated as

X=50+1*30=80

Hence for class B 80 or more will get grade A.

Q13. In class the z score at 20 calculated as

Z=(20-50)/10=-3

Hence by emperical rule of standard deviation data lies within -+3 standard deviatondeis 99.7 hence score more than 20 , 0.9985 proportion of student got more than 20 .

Since total no of students are 100 hence 100*0.9985=99.85 hence almost all student got score more than 20.

Similarly for class B

Z=(20-50)/30= -1

Hence since by emperical rule of standard deviation score Within +-1 68 % of date lies within. Hence Proportion of are lies more than 20 is 0.84 .

Since total no studentasare 100 hence 100*0.84 =84 students got more than 20.

Q14.since mean for both classes is 50 hence by emperical rule of standard deviation and symmetricity of distribution 50 % of data lies above and less to score 50.

Hence 50 % of data lies above 50.

Since 100 students are in both classes hence

100*0.50 = 50 , so 50 students in both classes got more than 50.

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