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In: Statistics and Probability

A new casino game involves rolling 3 dice. The winnings are directly proportional to the total...

A new casino game involves rolling 3 dice. The winnings are directly proportional to the total number of sixes rolled. Suppose a gambler brings his own dice and plays the game 100 times, with the following observed results (number of sixes, number of rolls): (0, 48), (1, 35), (2, 15), (3, 3). The casino becomes suspicious of the gambler and asks you to determine whether the dice are fair. If the dice are fair, you would expect the probability of rolling a 6 on any given toss to be 1/6. Assuming that the number of sixes in the three rolls are independent, the number of sixes in three rolls should follow a Binomial Distribution with n=3 and p=1/6. Using a level of significance of 0.01, what is the critical statistical value to determine whether or not the binomial distribution is a good fit for this data? Report answer to 3 significant figures.

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orchestra answered 2 years ago
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