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

To draw the Normal model, we use the mean of 72 as the center and the standard deviation of 6.9 to create a bell-shaped curve. The z-scores for 85.8 and 92.7 are calculated as:

z1 = (85.8 - 72) / 6.9 = 1.96
z2 = (92.7 - 72) / 6.9 = 2.90

Using a standard Normal table or calculator, we can find the area under the curve between these z-scores to find the percentage of scores between 85.8 and 92.7:

P(1.96 ≤ Z ≤ 2.90) = P(Z ≤ 2.90) - P(Z ≤ 1.96) ≈ 0.9881 - 0.9750 ≈ 0.0131

This means that about 1.31% of scores should be between 85.8 and 92.7 points. The closest choice is C) 2.35%, which is the best choice.

An English Instructor Gave a Final Exam and Found a Mean