Question

Math

Posted 6 months ago

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For sample size 1, the sampling distribution of the mean will be normally distributed
a. only if the population values are positive.
b. regardless of the shape of the population.
c. only if the shape of the population is symmetrical.
d. only if the population is normally distributed
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

For a sample size of 1, the sampling distribution of the mean is exactly the same as the population distribution. This is because each sample is just one observation, and therefore, the sample mean is equal to the value of that single observation

step 3

Therefore, the sampling distribution of the mean for a sample size of 1 will be normally distributed only if the population itself is normally distributed

1 Answer

D

Key Concept

Central Limit Theorem

Explanation

The central limit theorem applies when the sample size is large. For a sample size of 1, the sampling distribution of the mean is the same as the population distribution, and it will only be normally distributed if the population itself is normally distributed.

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