The mean score on a political attitude scale is 5 and the standard deviation is 2. The distribution is normal. Using the percentage approximations for the normal curve, how many people would get a score between 5 and 9?
A)34%
B)34% + 14% = 48%
C)50%
D)34% + 34% = 68%

Question

Quizplus · Accepted Answer

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean in a normal distribution. In this case, one standard deviation above the mean is 7 and one standard deviation below the mean is 3. Therefore, approximately 34% of the data falls between the mean of 5 and one standard deviation above the mean at 7. To find the percentage of people who scored between 5 and 9, we need to add the percentage of people who scored between the mean and one standard deviation above the mean (34%) with the percentage of people who scored between one standard deviation above the mean and two standard deviations above the mean (which is approximately 14%). This gives us a total of 48%, which is the closest answer choice.

The Mean Score on a Political Attitude Scale Is 5