Chapter 10, Problem AP3.4CPT

To determine

To find out from the options that about what percent of students at the college are on probation or on the dean’s list.

Answer to Problem AP3.4CPT

Option (c) is the correct option.

Explanation of Solution

It is given in the question that the distribution is approximately normal distribution. Also, it is given that:

  $\begin{array}{l}\mu =\text{Mean}=2.5\\ \sigma =\text{Standard deviation}=0.6\\ x=1\text{ or 3}\text{.5}\end{array}$

Now, we will calculate the z -score. It is the value decreased by the mean and divided by the standard deviation.

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ =\frac{3.5-2.5}{0.6}\\ =1.67\\ z=\frac{x-\mu }{\sigma }\\ =\frac{1.0-2.5}{0.6}\\ =-2.50\end{array}$

Now, to find out the corresponding probability using the normal probability table, we have,

  $\begin{array}{l}P(X\le 1.0\text{ or }X\ge 3.5)\\ =P(Z<-2.50)+P(Z>1.67)\\ =P(Z<-2.50)+1-P(Z>1.67)\\ =0.0062+1-0.9525\\ =0.0537\\ =5.37\%\\ \approx 5.4\%\end{array}$

Thus, we conclude that about $5.4\%$ of the students at the college are on probation or on the dean’s list. Therefore, option (c) is the correct option.