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

The Central Limit Theorem estabilishes 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.

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

akposevictor akposevictor · Answer 2 · 2021-11-25T14:59:46+01:00

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:

Based on the Central Limit Theorem, the sampling distribution of the sample mean for either skewed variable or normally distributed variable can be approximated to a normal distribution given the mean and standard deviation.

The central Limit Theorem holds true provided, n greater than or equal to 30.

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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https://brainly.com/question/17038949