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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 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.

Not sure if I am on the right track or not, But I concluded that the deviation is sqrt 33.3 (1-1/6)=5.27

With that 5.27 I multiplied by 1.5 and -1.5 to get +-7.9

With that I took 33.3-7.9 for minimum which was 25.4 and maximum I took 33.3+7.9 which gave me 41.2.

Please let me know if there are any errors with my method.

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