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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?

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Answer:

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

Step-by-step explanation:

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

  • [tex]\displaystyle z=\frac{1.23-2.52}{.43} = \frac{-1.29}{.43}= -3[/tex]
  • [tex]\displaystyle z=\frac{3.81-2.52}{.43}= \frac{1.29}{.43} =3[/tex]

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%.

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