1) In a simple game, a six-sided die is rolled 4 times. If all four rolls result

Question

1) In a simple game, a six-sided die is rolled 4 times.  If all four rolls result in either 1 or 2, then the player wins $50 dollars.  If the player has to pay $10 to play the game, what are the expected winnings of the player over time if many games are played?

2) The scores on a particular test are normally distributed with mean of 73 and standard deviation 5.  What score would a student need to be among the top 10% of all test scores?

3) What are the similarities and the differences between the family of t distributions and the standard normal distribution?

Explanation / Answer

1)

The probability of getting a 1 or a 2 on each roll is 2/6 = 1/3.

Since each roll is independent, the probability of getting a 1 or a 2 on all 4 rolls is (1/3)4 = 1/81.

So he has a 1 in 81 chance of winning $50. So the expected value of each game is $50 / 81 = $0.62.

If he has to pay $10 to win $0.62, then he is going to lose money quickly.

2)

mean = 73 , s = 5

z value at 10% = 1.2815

x = mean + z * s

= 73 + 1.2815 * 5

= 79.4075

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