Chapter 12.1, Problem 28AYU

Putting It Together: Weldon’s Dice On February 2, 1894, Frank Raphael Weldon wrote a letter to Francis Galton that included the results of 26,306 rolls of 12 dice. Weldon recorded the results such that a roll of a 5 or 6 resulted in a success, while a roll of 1, 2, 3, or 4 was a failure. The number of successes in each roll of the 12 dice are recorded in the table.

1. a. What is the probability of rolling a 5 or 6 when throwing a six-sided fair die?
2. b. Treating the probability determined in part (a) as the probability of success, compute the theoretical probability of 0, 1, 2, …, 12 successes in throwing 12 dice.
3. c. Use the probabilities found in part (b) to determine the expected frequency in observing 0, 1, 2, …, 12 successes after throwing the 12 dice 26,306 times.
4. d. Conduct a goodness-of-fit test to determine if the number of successes follows a binomial probability distribution.