Question

Suppose that you roll 117 fair six-sided dice. Find the probability that the sum of the dice is less than 400. (Round your answers to four decimal places.)

Answer 1

Answer:

The probability that the sum of the dice is less than 400 is 0.3050.

Step-by-step explanation:

Let X = outcomes of a single roll of a dice.

The possible outcomes of X are

S = {1, 2, 3, 4, 5, 6}

The probability of the random variable X is:

$P(X)=p=\frac{1}{6}=0.167$

Compute the mean and variance of the random variable X as follows:

$E(X)=\sum x.P(X=x)=3.5\\V(X)=E(X^{2})-(E(X))^{2}=2.917$

The dice was rolled n = 117 times.

The sum of the values of X in these 117 rolls follows a Normal distribution with mean 3.5 and variance 2.917.

Compute the probability that the sum of the dice is less than 400 as follows:

$P(\sum X$

*Use the z-table for the probability.

Thus, the probability that the sum of the dice is less than 400 is 0.3050.