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At one college, GPAs are normally distributed with a mean of 2.4 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.3 and 3?

A. 38.8
B. 78.2
C. 88.5
D. 46.4

Answer :

Final answer:

To find the percentage of students with a GPA between 2.3 and 3, calculate the Z-scores and use the standard normal distribution.

Explanation:

To find the percentage of students at the college with a GPA between 2.3 and 3, we can use the Z-score formula and the properties of the standard normal distribution.

  1. First, we calculate the Z-scores for the GPA values 2.3 and 3 using the formula: Z = (X - μ) / σ, where X is the GPA value, μ is the mean, and σ is the standard deviation.
  2. Next, we use a Z-table or a calculator to find the area under the standard normal distribution curve between these two Z-scores. This represents the percentage of students with a GPA between 2.3 and 3.
  3. Finally, we subtract this percentage from 1 to find the percentage of students who do not have a GPA between 2.3 and 3.

Using these steps, we find that the percentage of students at the college with a GPA between 2.3 and 3 is approximately 88.5%, so the correct answer is C.

Learn more about GPA distribution here:

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