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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:________

User BigbangO
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1 Answer

3 votes

Answer:

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

b. 4.5

Explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
\mu and standard deviation
\sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
\mu and standard deviation
s = (\sigma)/(√(n)).

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
\mu = 4.5, \sigma = 2.291

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
s = (2.291)/(√(36)) = 0.3818

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.

User RexE
by
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