The grade point averages (GPAs) of a large population of

Step 1 of 2

We have to find the fraction of the students that possess GPA above 3.0

Given that the college students are normally distributed with mean 2.4 and standard deviation 0.8

Then 

\(\begin{array}{l}
\mu=2.4 \\
\sigma=0.8
\end{array}\)

a) We have find \(P(X>3)\) by using standard normal tables

 Now

\(\begin{aligned}
Z & =\frac{\bar{X}-\mu}{\sigma} \\
& =(3-2.4) / 0.8 \\
& =0.75
\end{aligned}\)

Now

\(\begin{aligned}
P(Z>0.75) & =1-P(Z \leq 0.75) \\
& =1-0.77337 \\
& =0.22663
\end{aligned}\)

Hence P(X > 3) = 0.22663