In a game of luck, a turn consists of a player rolling 121212 fair 666-sided dice. Let X=X=X, equals the number of dice that land showing "111" in a turn. Find the mean and standard deviation of XXX.

mean = 2

standard deviation = 1.3

Step-by-step explanation:

For a binomial random variable X, we can use this formula for mean:

meanX = np

We use this formula for the standard deviation:

sdX = sqrt(np(1 - p))

Since a turn consists of rolling 12 dice, we have n = 12.

The dice are fair and 6-sided, so the probability that each die lands showing "1" is p = 1/6.

meanX = np

= (12)(1/6)

= 2 dice

sdX = sqrt(np(1 - p))

= sqrt((12)(1/6)(5/6))

≈ sqrt(1.667)

≈ 1.291 dice

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