Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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?

Sagot :

Supernova

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%.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.