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.)

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:

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

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:

*Use the z-table for the probability.

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

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