I Give You a Die, and You Roll It 600

question 43

Multiple Choice

I give you a die, and you roll it 600 times. Let X = the number of ones observed in those 600 rolls. You build the following line of reasoning:
Steps
1) You assume each roll is an independent, random outcome.
2) You assume the dice is fair.
3) Using your statistics book, you conclude that X is distributed binomial with mean 100 and variance 83.
4) Based on this distribution, you conclude that you would observe X < 82 or X > 118 approximately 5% of the time.
5) You observe X = 123 and conclude that the probability that X < 82 or X > 118 is not 5%.
6) Because the probability that X < 82 or X > 118 is not 5%, you conclude the die is not fair.
Which of these steps is part of inductive reasoning?

• A) Step 5
• B) Steps 4 and 6 only
• C) All 6 steps
• D) Steps 4, 5, and 6 only

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