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allsm [11]
3 years ago
9

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.a. exactly norm

al for large sample sizesb. approximately normal for all sample sizesc. exactly normal for all sample sizes
Mathematics
1 answer:
maxonik [38]3 years ago
7 0

Answer:

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 \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.

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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