Based on previous records,$17\%$ of the vehicles passing through a tollbooth have out-of-state plates. A bored tollbooth worker decides to pass the time by counting how many vehicles pass through until he sees two with out-of-state plates.$27$

(a) Describe the design of a simulation to estimate the average number of vehicles it takes to find two with out of- state plates. Explain clearly how you will use the partial table of random digits below to carry out your simulation.

(b) Perform three repetitions of the simulation you described in part (a). Copy the random digits below onto your paper. Then mark on or directly above the table to show your results.

Out-of-state plates are found on$17\%$ of vehicles passing through a tollbooth. A bored tollbooth worker kills time by counting the number of automobiles passing through until he notices two with out-of-state plates.

According to previous figures, $17\%$ of vehicles travelling through a tollbooth have out-of-state plates in the question. As a result, we'll employ two-digit numbers. Then we'll pick a row from table D. After that, choose the first two-digit number. If the number is between $00$ and $16$, a car with out-of-state plates has passed through the toll booth; otherwise, disregard the number. Then we'll do it all over again until you get the first number between $00$ and $16$. We'll repeat this process until you get the second number between $00$ and $16$. As a result, the time is the number of digits required to get two numbers between $00$ and $16$. As a result, we'll run the simulation numerous times and average the results.

According to previous figures, $17\%$of vehicles travelling through a tollbooth have out-of-state plates in the question. As a result, we'll employ two-digit numbers. Then we'll pick a row from table D. After that, choose the first two-digit number. If the number is between $00$and $16$, a car with out-of-state plates has passed through the toll booth; otherwise, disregard the number. Then we'll do it again until you get the first number between$00$and $16$. We'll repeat this process until you get the second number between $00$and $16$. As a result, the time is the number of numbers required to achieve two numbers between 00 and 16 until the second number between $00$and $16$is received. As a result, the first simulation will take place.

As a result, three integers were required, and the time was calculated. The second simulation will be as follows:

$$\begin{gathered} 20\Rightarrow Ignore \\ 31\Rightarrow Ignore \\ 06\Rightarrow Firstcar \\ 44\Rightarrow Ignore \\ 90\Rightarrow Ignore \end{gathered}$$

As a result, three numbers were required, and the time was $14$minutes. Finally, the final simulation will be as follows:

As a result, three numbers were required, and the time was $13$ minutes.