Chapter 10, Problem 20PT3

To determine

To find: Maximum average a student can attain and get an F.

Answer to Problem 20PT3

Option C is the correct choice.

Explanation of Solution

Given information:

Mean of grades of a class $=76$

Standard deviation of final grades of a class $=8$

Grade received by top $10\%$ students $=A$

Grade received by next $20\%$ students $=B$

Grade received by the next $40\%$ students $=C$

Grade received by the next $20\%$ students $=D$

Grade received by bottom $\text{1}0\%$ students $=F$

Calculation:

Let X be the distribution of grades.

  $\begin{array}{l}P(X\le x)=0.10\\ P\left(\frac{x-\mu }{\sigma }\le \frac{x-76}{8}\right)=0.10\end{array}$

From z tables,

  $P(z>1.2816)=0.10$

Then, as per symmetry of the normal distribution

  $P(z<-1.2816)=0.10$

Comparing the values

  $\begin{array}{l}-1.2816=\frac{x-76}{8}\\ x=76-8\times 1.2816=65.75\end{array}$