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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.

Short Answer

Expert verified

Part (a) We'll run the simulation several times to figure out the average time.

Part (b) Three numbers were needed and the time is 13

Step by step solution

01

Part (a) Step 1. Given

Out-of-state plates are found on17% 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.

02

Part (a) Step 2. Explanation

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.

03

Part (b) Step 1. Explanation

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 00and 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 between00and 16. We'll repeat this process until you get the second number between 00and 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 00and 16is received. As a result, the first simulation will take place.

41⇒Ignore05⇒Firstcar09⇒Secondcar

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

20⇒Ignore31⇒Ignore06⇒Firstcar44⇒Ignore90⇒Ignore

50⇒Ignore59⇒Ignore59⇒Ignore88⇒Ignore43⇒Ignore18⇒Ignore80⇒Ignore53⇒Ignore11⇒Secondcar

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

58⇒Ignore44⇒Ignore69⇒Ignore94⇒Ignore86⇒Ignore85⇒Ignore79⇒Ignore67⇒Ignore05⇒Firstcar81⇒Ignore18⇒Ignore45⇒Ignore14⇒Secondcar

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

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