Answer:
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))
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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
The mean and standard deviation of the game of luck are;
Mean = 2
Standard deviation = 1.29
We are told that a turn consists of rolling 12 fair six sided dice.
Thus;
n = 12
Probability of each one six sided die showing 1 is;
p = 1/6
Now,the formula for the mean is;
E(X) = np
Plugging in the relevant values gives;
E(X) = 12 × 1/6
E(X) = 2
Now, for the standard deviation, we will use the formula;
Standard deviation = √(np(1 - p))
Plugging in the relevant values;
Standard deviation = √((12 × 1/6)(1 - 1/6))
Standard deviation = 1.29
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