Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.592.59 and a standard deviation of 0.390.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.421.42 and 3.763.76?

Answer 1

Given,

Grade point averages of undergraduate students at one university have a bell-shaped distribution.

Mean = = 2.59

Standard deviation = = 0.39

According to Empirical rule ,

1) 68% of data falls within the first standard deviation from the mean.

2) 95% fall within two standard deviations.

3) 99.7% fall within three standard deviations.

We have to find percentage of the students have grade point averages that are between 1.42 and 3.76.

z score for 1.42 = ( x - ) / = ( 1.42 - 2.59 ) / 0.39 = -3

That is 1.42 is 3 standard deviation below mean.

z score for 3.76 = ( x - ) / = ( 3.76 - 2.59 ) / 0.39 = 3

That is 3.76 is 3 standard deviation above mean.

So , according to Empirical rule 99.7% of data fall within three standard deviations from the mean.

99.7% of the students have grade point averages that are between 1.42 and 3.76.