Question

Suppose you’re playing a dice game in which two 6-sided dice are thrown, and players win when the sum of the values appearing on the dice is at least 7. In the last 100 games, you’ve noticed that players have won 95 times. Do you have any reason to believe that the dice are unfairly weighted using the central limit theorem? I have understood up to getting z=7.434. But how do you know to find P(z>7.434) and not use P(x<7.434). Does P(z>7.434) give you the probability that you would win 95 or more times? or is it giving you the probability that you win exactly 95 times. Very specific question- thanks

Answer 1

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Answer:

Here lets first find the actual fair probability of getting a sum of atleast 7

=>

P(X = 7, 8, 9, 10, 11, 12)

= (6 + 5 + 4 + 3 + 2 + 1) / 36

= 0.583

But we are given that the observed probability in real case is 95/100 = 0.95

We are saying this is a right tailed test (z>(0.95-0.583/sqrt(0.583*(1-0.583/100)) = P(Z>7.44) becasue we want to test the fairness of 0.583 proabability. Since the observed(0.95) is greater than the actual 0.583 we use (P>7.44) . We test the fairness or biased case P(Z>7.44) when we have observed proportion greater than actual proportion.

Lastly P(z>7.434) give the probability that we would win 95 or more time (atleast 95 times)