Assume that a set of test scores in an Introduction to Finance class is normally distributed with a mean of 72 and a standard deviation of 8. Use the 68-95-99.7 rule to
Find the percentage of scores between 80 and 96.
A) 13.5%
B) 15.85%
C) 30.7%
D) 2.5%
E) 25.5%

Question

Quizplus · Accepted Answer

Using the 68-95-99.7 rule, we know that approximately 68% of the scores are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations. 
To find the percentage of scores between 80 and 96, we need to find the z-scores for each value using the formula: 
z = (x - μ) / σ 
For x = 80: z = (80 - 72) / 8 = 1 
For x = 96: z = (96 - 72) / 8 = 3 
Using a standard normal distribution table or calculator, we can find the percentage of scores between z = 1 and z = 3, which is approximately 15.85%. Therefore, the answer is B.

Assume That a Set of Test Scores in an Introduction