Question

At Springfield University, the grade point averages (GPA) of its 1000 undergraduate students are normally distributed with mean 2.83 and standard deviation 0.38. What percentage of the undergraduate students have GPAs below 2.00?

0.9855%

1.45%

98.55%

0.0145%

Answer 1

Given:

n = 1000

Mean(µ) = 2.83

Standard deviation(σ) = 0.38

To find: Percentage of the undergraduate students have GPA's below 2.00.

That is, to find P(x <= 2)

We need to find the Z score for finding the probability.

Following is the formula to find the Z score.

P(X <= 2) = P(Z <= -2.18421)

Now, we can find out this probability using Z table/ technology.

Suppose, we are using excel to find this probability.

Then, use the following excel command.

= NORMSDIST(Z)

=NORMSDIST(-2.18421)

We will get, P(X <= 2) = 0.014473.

That is, P(X <= 2) = 1.45%

Hence, option 2 is correct.

The percentage of the undergraduate students have GPAs below 2.00 is, 1.45%.