Question

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?

Answer 1

Answer:

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 $\mu$ 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 $s = \frac{\sigma}{\sqrt{n}}$.

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 $\mu = 650, \sigma = 24$.

Sample of 36:

This means that $n = 36, s = \frac{24}{\sqrt{36}} = 4$

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.