Provide an appropriate response.
-The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 10. Use the Empirical Rule to find the percentage of scores that lie between 60 and 80. (Assume the data set has a
Bell-shaped distribution.)
A)47.5%
B)68%
C)34%
D)95%

Question

Quizplus · Accepted Answer

According to the Empirical Rule (68-95-99.7 rule) for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean. In this case, one standard deviation from the mean (80) is 70 to 90. Therefore, half of this range (60 to 80, which is one standard deviation below the mean to the mean) represents half of 68%, which is 34%. However, since the question asks for the range from 60 to 80, we must also include the lower tail, which is an additional 13.5% (half of the 27% that falls outside one standard deviation on either side). Thus, the total percentage of scores between 60 and 80 is 34% + 13.5% = 47.5%.

Provide an Appropriate Response