Chapter 5.1, Problem 9E

(a)

To determine

To describe how to use a random number generator to perform one trial of the simulation.

Explanation of Solution

In this question, Luke’s teacher wants to take the test for its students by asking multiple choice questions. Now we have to use a random number generator to perform one trial of the simulation. That can be done by first we have ten multiple choice question with four options each. It is given that you pass if you answer six or more questions correctly. Since each one question has four answer options and since one of these answer options are correct, we have a one in four chance of selecting the correct answer option on a question when guessing. Let us use a random number generator to randomly generate ten digits from one to four where one represents a correct answer and $2,3,4$ represent an incorrect answer.

(b)

To determine

To explain what the dot at $1$ represents.

Answer to Problem 9E

There was one trial in the simulation that had one correct answer on the ten questions.

Explanation of Solution

In the question the dot plot is given which shows Luke’s simulated quiz score. The dots in the dot plot show the simulated quiz score on $50$ trials in the simulation. The dot at $1$ represents one trial that resulted in a quiz score of one. Or equivalently, there was one trial in the simulation that had one correct answer on the ten questions.

(c)

To determine

To use the results of the stimulation to estimate the probability that Luke passes the quiz.

Answer to Problem 9E

  $0.10$ .

Explanation of Solution

We have to find out the probability that Luke passes the quiz. Now, we have ten multiple choice question with four option each. It is given you pass the test if you answer six or more questions correctly. The dots in the dot plot shows the simulated quiz score on $50$ trials in the simulation. We then note that five dots lie above six and no dots lie to the right of six, which implies $5\text{ of the 50}$ trials results in a quiz score of at least $6$ . Thus, we have,

  $\begin{array}{l}\frac{5}{50}=\frac{1}{10}\\ =0.10\end{array}$

This then implies that the probability that Luke passes the quiz is about $0.10$ .

(d)

To determine

To explain is there a convincing evidence that he understands some of the material.

Answer to Problem 9E

Yes, there is convincing evidence that he understands some of the material.

Explanation of Solution

The dots in the dot plot show the simulated quiz score on $50$ trials in the simulation, assuming that the person is guessing the answer to each question. In the dot plot, we then note that there are no dots above $8$ nor to the right of $8$ , which implies that it is very unusual to get a quiz score of at least $8$ when you are making random guessing. This means that there is convincing evidence that he understands some of the material as it is unlikely that he was making random guesses on every question.