Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 1.23 and 3.81?

Answer 1

Using the Empirical Rule, we find that .997 (99.7%) of students have grade point averages that are between 1.23 and 3.81.

Explanation:

Calculate the z-scores corresponding to a GPA of 1.23 and 3.81.

• 
  `\displaystyle z=(1.23-2.52)/(.43) = (-1.29)/(.43)= -3`
• 
  `\displaystyle z=(3.81-2.52)/(.43)= (1.29)/(.43) =3`

We want to find the area between the z-scores of -3 and 3.

The Empirical Rule tells us that 99.7% of the data lies within three standard deviations under the normal curve.

Therefore, the area between -3 < z < 3 is about .997, or around 99.7%.