Chapter 5, Problem 14PT

(a)

To determine

To describe the design of a simulation to estimate the average number of vehicles it takes to find two with out-of-state plates and explain clearly hoe you will use the partial table of random digits below to carry out your simulation.

Explanation of Solution

In the question, based on the previous records, $\text{17\%}$ of the vehicles passing through a tollbooth have out-of-state plate. Thus, we will use two-digit numbers. Then, we will choose a row in table D. And select the first two-digit number. If the number is between $\text{00 and 16}$ , then a car passes through the toll booth that has out-of state plates, else ignore the number. And then, we will repeat until you obtain the first number between $\text{00 and 16}$ . And also we will repeat again until you obtain the second number between $\text{00 and 16}$ . Thus, the time is then the number of numbers needed two obtain two numbers between $\text{00 and 16}$ . Therefore, we will repeat the simulation multiple times and determine the average time.

(b)

To determine

To perform three repetitions of the simulation you described in part (a).

Explanation of Solution

In the question, based on the previous records, $\text{17\%}$ of the vehicles passing through a tollbooth have out-of-state plate. Thus, we will use two-digit numbers. Then, we will choose a row in table D. And select the first two-digit number. If the number is between $\text{00 and 16}$ , then a car passes through the toll booth that has out-of state plates, else ignore the number. And then, we will repeat until you obtain the first number between $\text{00 and 16}$ . And also we will repeat again until you obtain the second number between $\text{00 and 16}$ . Thus, the time is then the number of numbers needed two obtain two numbers between $\text{00 and 16}$ until you obtained the second number between $\text{00 and 16}$ . Thus, the first simulation will be as:

  $\begin{array}{l}\text{41}\Rightarrow \text{ Ignore}\\ 05\Rightarrow \text{ First car}\\ 09\Rightarrow \text{ Second car}\end{array}$

Thus, three numbers were needed and thus the time is $\text{3}$ . Now, the second simulation will be:

  $\begin{array}{l}20\Rightarrow \text{ Ignore}\\ 31\Rightarrow \text{ Ignore}\\ 06\Rightarrow \text{ First car}\\ 44\Rightarrow \text{ Ignore}\\ 90\Rightarrow \text{ Ignore}\\ 50\Rightarrow \text{ Ignore}\\ 59\Rightarrow \text{ Ignore}\\ 59\Rightarrow \text{ Ignore}\\ 88\Rightarrow \text{ Ignore}\\ 43\Rightarrow \text{ Ignore}\\ 18\Rightarrow \text{ Ignore}\\ 80\Rightarrow \text{ Ignore}\\ 53\Rightarrow \text{ Ignore}\\ 11\Rightarrow \text{ Second car}\end{array}$

Thus, three numbers were needed and thus the time is $14$ . At last the third simulation will be as:

  $\begin{array}{l}58\Rightarrow \text{ Ignore}\\ 44\Rightarrow \text{ Ignore}\\ 69\Rightarrow \text{ Ignore}\\ 94\Rightarrow \text{ Ignore}\\ 86\Rightarrow \text{ Ignore}\\ 85\Rightarrow \text{ Ignore}\\ 79\Rightarrow \text{ Ignore}\\ 67\Rightarrow \text{ Ignore}\\ 05\Rightarrow \text{ First car}\\ 81\Rightarrow \text{ Ignore}\\ 18\Rightarrow \text{ Ignore}\\ 45\Rightarrow \text{ Ignore}\\ 14\Rightarrow \text{ Second car}\end{array}$

Thus, three numbers were needed and thus the time is $13$ .