Question

The grades on the last art exam had a mean of 75%. Assuming a normal distribution with a standard deviation of 7%, what percentage of students are expected to earn a score between 75% and 82% based on the empirical rule?a) 68%

b) 16%
c) 32%
d) 34%

Answer 1

Approximately 34% of students are expected to earn a score between 75% and 82% on an art exam with a mean of 75% and a standard deviation of 7%, assuming normal distribution.

Step-by-step explanation:

The student asked about the percentage of students expected to earn a score between 75% and 82% on an art exam, given a mean score of 75%, a standard deviation of 7%, and assuming a normal distribution. According to the empirical rule (also known as the 68-95-99.7 rule), approximately 68% of values fall within one standard deviation of the mean in a normal distribution. Since 82% is one standard deviation above the mean (75% + 7%), and the question asks about the range from the mean to one standard deviation above it, we can conclude that approximately 34% of the students scored between these two values (half of 68%).