An English instructor gave a final exam and found a mean score of 72 points and a standard deviation of 6.9 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.What percent of scores should be between 85.8 and 92.7 points?
A) ;5%
B) ;2.5%
C) ;2.35%
D) ;4.7%
E) ;35.9318841%

Question

An English instructor gave a final exam and found a mean score of 72 points and a standard deviation of 6.9 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.What percent of scores should be between 85.8 and 92.7 points?
A) ;5% 
B) ;2.5% 
C) ;2.35% 
D) ;4.7% 
E) ;35.9318841%

Quizplus · Accepted Answer

We are given mean = 72 and standard deviation = 6.9
Drawing the Normal Model,

![Normal Model](https://i.imgur.com/vBRIABI.png)

We need to find P(85.8 < X < 92.7)
Converting to z-score:

z1 = (85.8 - 72)/6.9 = 1.913
z2 = (92.7 - 72)/6.9 = 2.899

Using the Z-table or calculator, we find:
P(1.913 < Z < 2.899) = 0.0235

Converting back to exam scores,
P(85.8 < X < 92.7) = 0.0235 * 100% = 2.35%

Therefore, the best choice is C (2.35%).

An English Instructor Gave a Final Exam and Found a Mean