1. A True/False quiz consists of 8 questions.
(a) What assumptions will you make to do this simulation?
The probability of getting one question correct is independent of the probability of getting another question correct.
The probability of getting a question correct is = 1/2 and is the same for each question.
(b) How would you use the calculator to model this problem?
Explain what one trial consists of in this problem.
Do 17 trials and record your results on the frequency table.
Since it’s a true/false question we have a 50% chance of getting a problem right. We will need to use any numbers we want and let half of them represent getting the question right and the other half represents getting the question wrong.
Use the random number generator. Let 0 represent getting the question wrong and let 1 represent getting the question right. Generate 8 random numbers from 0 to 1 and record your results on the frequency table. These 8 numbers are one trial.
*Answers may vary.

2. (c) How would you use the following random number table to model this problem? Explain what one trial consists of in this problem. Clearly show 3 trials on the random number table and record your response on the frequency table.
In this table we have digits 0-9, so again half of those digits need to represent getting the question right and the other half represents getting the question wrong.
So, for example let the even numbers represent getting the question correct and the odd digits represent getting the question wrong. Select 8 digits to represent the 8 questions on the quiz and record your results. These 8 digits are one trial.
*Answers may vary.
Number of Problems answered correctly
Frequency

3. (d) Based on your simulation, estimate the probability of answering at least 3 problems correctly.
 By looking at the frequency table we can see that the probability of at least 3 correct = 19/20   
(e) Based on your simulation, estimate the probability of answering at most 4 problems correctly.
 P(at most 4 questions correct) = 14/20
(f) Based on the information given (theoretically),
estimate the average number of questions a student will
answer correctly by guessing.
 8(1/2) = 4 questions correct
(g) Based on your simulation, estimate the average
number of questions a student will answer correctly
by guessing.
Using the frequency table and the formula
we find the average by adding up all the x*p(x)

4. Passing Game A quarterback on a football team completes 35% of his passes. Suppose he passes 10 times in a game.
(a) What assumptions will you make to do this simulation?
1) The probability of completing one pass is independent of the probability of completing another pass.
2) The probability of completing a pass is 0.35 and is the same for each pass.
(b) How would you use the calculator to model this problem?
Use the random # generator. Let the number 1-35 represent a completed pass and the numbers represent an incomplete pass. Select 10 numbers from (1- to 100) to present the 10 passes. These 10 numbers are one trial. *answers may vary
(c) How would you use the following random number table to model this problem? Explain what one trial consists of in this problem. Perform 3 trials.
This one gets a little tricky, because you have to distinguish between the single digit numbers like 1 and 2, versus the double digits numbers (11,12 …) and even the triple digit number 100.

5. (c) How would you use the following random number table to model this problem? Explain what one trial consists of in this problem. Perform 3 trials.
So to make it easier we will do this: Let represent a completed pass and the represent an incomplete pass. Select 10 Double-digit numbers from (00-99) to present the 10 passes. These 10 numbers are one trial. *answers may vary

6. 3. Driving test. At the local DPS about 80% of the people pass the driving test. Suppose there are 8 people at the DPS today. (a) Suppose you let #1-8 represent passing the driving test and #9,0 represent failing the test. You select 8 single digit numbers to represent one trial. Interpret this trial: {1, 6, 8, 1, 3, 8, 4, 0} 7 out of 8 people passed the driving test (b) Suppose that only 75% of the people pass the driving test and that there are only 6 people at the DPS. How would you use a calculator to model this problem? Show an example of a trial. Let 1-75 represent passing the test and represent failing the test. Select 6 numbers from to represent the 6 people at the DPS. Answers may vary.

7. 3. Driving test. At the local DPS about 80% of the people pass the driving test. Suppose there are 8 people at the DPS today.
(c) Suppose that only 60% of the people pass the driving test but there are 10 people at the DPS. How would you use the following random number table to model this problem? Clearly show 3 trials on the random number table below.
Let 0-5 represent passing the test and 6-9 represent failing the test. Select 10 single-digit numbers to represent the 10 people at the DPS.