Suppose you were to draw all possible samples of size 36 from a large population with a mean of 650 and a standard deviation of 24. You then compute the sample mean x-bar for each sample. From the long list of sample means, you create the sampling distribution of the sample mean, assigning probabilities to all possible values of x-bar. Required:
What is the shape of the sampling distribution you would expect to produce?

By the Central Limit Theorem, it is approximately normal with mean 650 and standard deviation 4.

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 650 and a standard deviation of 24.

This means that .

Sample of 36:

This means that

What is the shape of the sampling distribution you would expect to produce?

By the Central Limit Theorem, it is approximately normal with mean 650 and standard deviation 4.

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