Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.53 and a standard deviation of 0.41. Using the empirical rule, what percentage of the students have grade point averages that are greater than 2.94? Please do not round your answer.

Answer 1

Given,

= 2.53 , = 0.41

z-score = (x - ) / ​​​​​​

= ( 2.94 - 2.53) / 0.41

= 1

That is 2.94 is 1 standard deviation above the mean.

Using empirical rule, approximately 68% of the data falls in 1 standard deviation of the mean.

That is 1 - 0.68 = 32% data falls outside of 1 standard deviation of the mean and 16% data falls either

side of outside region.

So,

P(X > 2.94) = 16%