Fair 6-sided die (Probability)

Algebra
Tutor: None Selected Time limit: 1 Day

On a fair 6-sided die, each number has an equal probability 'p' of being rolled. When a fair die is rolled 'n' times, the most likely outcome (the mean) is that each number will be rolled 'np' times, with a standard deviation of SD = SQRT(np(1 - p)). Brandon rolls a die 200 times. He will conclude that the die is loaded (unfair) if the number of times any number is rolled is outside 1.5 standard deviations of the mean. What are the minimum and maximum number of times a number can be rolled without Brandon concluding that the die is loaded?

May 17th, 2015

n = 200

p = 1/6

SD = (200*1/6*(1-1/16))^2 = 5.27

1.5 * 5.27 = +/- 7.9

If rolled 200 times, the mean is = 200*1/6=33.3

33.3 + 7.9 = 41.2 maximum

33.3 - 7.9 = 25.4 minimum

Hope that helps!

May 17th, 2015

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