Rolling a fair Eight-sided die produces a uniformly distributed set of numbers between 1 and 8 with a mean of 4.5 and a standard deviation of 2.291. Assume that n eight-sided dice are rolled many times and the mean of the n outcomes is computed each time. Required:
a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.
b. The mean of the resulting distribution of the sample means is:

a. The mean is 4.5 and the standard deviation is 0.3818.

b. 4.5

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 4.5 and a standard deviation of 2.291.

This means that

a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.

By the Central Limit Theorem, the mean is 4.5 and the standard deviation is

The mean is 4.5 and the standard deviation is 0.3818.

b. The mean of the resulting distribution of the sample means is:________

By the Central Limit Theorem, 4.5.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: