For a population with an unknown distribution, the form of the sampling distribution of the sample mean is .a. exactly normal for large sample sizesb. approximately normal for all sample sizesc. exactly normal for all sample sizes

For a population where the distribution is unknown, the sampling distribution of the sample mean will be: b. approximately normal for all sample sizes

Recall:

Therefore, for a population where the distribution is unknown, the sampling distribution of the sample mean will be: b. approximately normal for all sample sizes

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Approximately normal for large sample sizes

Step-by-step explanation:

The Central Limit Theorem estabilishes 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.

In this question:

The distribution is unknown, so the sampling distribution will only be approximately normal when n is at least 30.

So the correct answer should be:

Approximately normal for large sample sizes

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