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The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard deviation of the distribution of sample means for samples of size 60

User Ozandlb
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Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

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.

Standard deviation is 9.5 for a population.

This means that
\sigma = 9.5

Sample of 60:

This means that
n = 60

What is the standard deviation of the distribution of sample means for samples of size 60?


s = (\sigma)/(√(n)) = (9.5)/(√(60)) = 1.2264

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

User Snowdude
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