Question

The distribution of grade point averages (GPAs) for a certain college is approximately Normal with a mean of $2.5$ and a standard deviation of $0.6.$ The minimum possible GPA is 0.0 and the maximum possible GPA is $4.33$. Any student with a GPA less than $1.0$ is put on probation, while any student with a GPA of 3.5 or higher is on the dean’s list. About what percent of students at the college are on probation or on the dean’s list?

$$\begin{gathered} a.0.6 \\ b.4.7 \\ c.5.4 \\ d.94.6 \\ e.95.3 \end{gathered}$$

Short answer

The correct option is:

$c.5.4$percent of students at the college are on probation or on the dean’s list

Step-by-step solution

 Step 1: Given information 

We have to tell percent of students at the college are on probation or on the dean’s list.

Explanation 

The college are on probabtion:

$P(X\le 1.0\text{or}X\ge 3.5)=P(Z<-2.50\text{or}Z>1.67)$

$=P(Z<-2.50)+1-P(Z<1.67)$

$=0.0062+1-0.9525$

$=5.4\%$