Data Analysis Assignment 2

Probability and Expected Value (Chapters 4 and 5)

1.Go to the website www.random.org.

Under "Free Services", click on Dice Roller. For the number of virtual dice that you want to roll, select 25. Then click Roll Dice.

Take a screenshot or picture of your results, and paste it into the space below.

My dice are as follows 1, 5, 1, 1, 2, 2, 2, 6, 3, 5, 6, 5, 3, 3, 2, 6, 3, 6, 1, 6, 4, 4, 5, 1, 3

2.Count how many times each number appeared, and fill in the frequency table and relative frequency (probability) table below with your results.

Use your results in the table to calculate the following relative frequency probabilities. Show your calculations.

3.What is the probability of rolling an even number?

4+2+5=11. 11/25=0.44, 44%

4.What is the probability of rolling a number that is even OR a 5?

4+2+5+4=15, 15/25=0.60, 60%

5.What is the probability of rolling a number that is not 5?

25-4=21, 21/25=0.84, 84%

6.If you roll two dice, what is the probability that both of them are 5?

7.If you roll two dice, what is the probability that at least one of them is a 5?

In a classical probability assessment, the probability of rolling each number is 1/6. Use this to calculate the following classical probabilities. Show your calculations.

8.What is the probability of rolling an even number?

9.What is the probability of rolling a number that is even OR a 5?

10.What is the probability of rolling a number that is not 5?

11.If you roll two dice, what is the probability that both of them are 5?

12.If you roll two dice, what is the probability that at least one of them is a 5?

The probability distribution for rolling one die is below.

Number on the Die

Probability

1

1/6

2

1/6

3

1/6

4

1/6

5

1/6

6

1/6

13.Use the table to calculate the expected value of one die roll. Show your calculations.

14.Use the table and the expected value to calculate the standard deviation of one die roll. Show your calculations.

Use Minitab to answer the questions below.

15.The probability of rolling an even number on a die is 0.5. If you roll 25 dice, what is the probability that you get 15 or more even numbers? Paste your distribution plot in the space below.

16.The probability of rolling an even number on a die is 0.5. If you roll 25 dice, what is the probability that you get less than 10 even numbers? (Hint: be careful, the x value here is not 10) Paste your distribution plot in the space below.

17.The probability of rolling an even number on a die is 0.5. If you roll 25 dice, what is the probability that you get between 8 and 16 even numbers? Paste your distribution plot in the space below.

18.The probability of rolling an even number on a die is 0.5. If you roll 25 dice, what is the probability that you get exactly 20 even numbers? Paste your distribution plot in the space below.

19. Of the four events in questions 15-18, which event is most likely to happen? How do you know?

20.Of the four events in questions 15-18, which event is least likely to happen? How do you know?

Save your Word document solutions and your Minitab Project results (go to File - Save...)

To turn in this assignment, go to the Data Analysis Assignment 2 folder on Blackboard. Click on the Data Analysis Assignment 2 submission link at the bottom. Under Assignment Submission, attach both documents (using Browse My Computer). Then click Submit.