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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?

Respuesta :

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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 [tex]\mu = 650, \sigma = 24[/tex].

Sample of 36:

This means that [tex]n = 36, s = \frac{24}{\sqrt{36}} = 4[/tex]

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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