Question: You have five dice, like in a game of Yahtzee! Suppose you roll the five...

Question:

You have five dice, like in a game of Yahtzee! Suppose you roll the five dice once and sum the numbers the five dice show.

(a) What is the mean and the standard deviation of the sum of five dice?

(b) Suppose you average 60 of such rolls with the five dice. What is the distribution of this average?

Solutions

Expert Solution

When we roll a fair die possible outcome are 1, 2, 3, 4, 5, and 6. Since each outcome is equally likely so the probability of each outcome is 1/6 .

Following table shows the calculations:

Xi	P(Xi=xi)	Xi*P(X1=xi)	Xi^2*P(Xi=xi)
1	1/6	0.166666667	0.166666667
2	1/6	0.333333333	0.666666667
3	1/6	0.5	1.5
4	1/6	0.666666667	2.666666667
5	1/6	0.833333333	4.166666667
6	1/6	1	6
Total		3.5	15.16666667

So,

and

We roll five dice and let outcome of five dice are shown by X1, X2, X3, X4 and X5.

Let X= X1+X2+X3+X4+X5

The mean of the sum of five dice is

The standard deviation of the sum of five dice is

(b)

(c)

orchestra answered 1 year ago

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