Question

Suppose grade point averages have a bell-shaped distribution with a mean of 2.53 and standard deviation of 0.4. Use empirical rule, what percentage have averages greater than 2.13?

a) 16%
b) 34%
c) 84%
d) 50%

Answer 1

Approximately 2.5 percent of the students have averages greater than 2.13

Step-by-step explanation:

The empirical rule states that in a bell-shaped distribution, approximately 68 percent of the data falls within one standard deviation of the mean, approximately 95 percent of the data falls within two standard deviations of the mean, and more than 99 percent of the data falls within three standard deviations of the mean.

In this case, the mean is 2.53 and the standard deviation is 0.4.

To find the percentage of students with averages greater than 2.13, we need to find the percentage of data that falls beyond two standard deviations below the mean (2.13 - 2.53 = -0.4).

Since the data is symmetric, the same percentage of data falls beyond two standard deviations above the mean as below. Therefore, the percentage of students with averages greater than 2.13 is approximately 2.5 percent.