Chapter 11.5, Problem 13PPSE

Solution

To state: The average number of correct answers for the trials and the number of trials of simulation that must be conducted if a person has to take a multiple-choice quiz and there are 4 choices for each question. The person doesn’t know the answer to the last 5 questions, so guess the answers.

The simulation results are:

  $\begin{array}{l}31242412113414141212233422324213412\\ 113134243332334\text{}31234133144143223413\\ 42322143311222412232312322222331233\\ 11214332433341421224341124343214234\end{array}$

The average number of correct answer for these trials is about $1.14$ and the number of trials of the simulation conducted is 28.

Given information:

There are 24 a person has to take a multiple-choice quiz and there are 4 choices for each question. The person doesn’t know the answer to the last 5 questions, so guess the answers. The

Simulation results are:

  $\begin{array}{l}31242412113414141212233422324213412\\ 113134243332334\text{}31234133144143223413\\ 42322143311222412232312322222331233\\ 11214332433341421224341124343214234\end{array}$

Explanation:

Consider the random table shown below:

  $\begin{array}{l}\underset{1}{\underbrace{31242}}\underset{3}{\underbrace{41211}}\underset{2}{\underbrace{34141}}\underset{2}{\underbrace{41212}}2334223242\underset{2}{\underbrace{13412}}\\ \underset{3}{\underbrace{11313}}4243332334\text{}\underset{1}{\underbrace{31234}}\underset{2}{\underbrace{13314}}\underset{1}{\underbrace{41432}}\underset{1}{\underbrace{23413}}\\ 42322\underset{2}{\underbrace{14331}}\underset{1}{\underbrace{12224}}\underset{1}{\underbrace{12232}}\underset{1}{\underbrace{31232}}22223\underset{1}{\underbrace{31233}}\\ \underset{3}{\underbrace{11214}}33243\underset{1}{\underbrace{33414}}\underset{1}{\underbrace{21224}}\underset{2}{\underbrace{34112}}43432\underset{1}{\underbrace{14234}}\end{array}$

In each group, there are 5 numbers, number 1 represents the correct answer and the remaining numbers represents the incorrect answer.

From the above table, it can be seen that the number of group is 28, so the number of trials of the simulation conducted is 28.

Now find the average by dividing the total number 1(32) by the total number of trials.

  $\begin{array}{c}\text{Average}=\frac{1+3+2+2+2+3+1+2+1+1+2+1+1+1+1+3+1+1+2+1}{28}\\ =\frac{32}{28}\\ \approx 1.14\end{array}$

Therefore, the average number of correct answer for these trials is about $1.14$ .