Question

suppose that we will randomly select a sample of 109 measurements from a population having a mean equal to 21 and a standard deviation equal to 8. (a) describe the shape of the sampling distribution of the sample mean . do we need to make any assumptions about the shape of the population? why or why not?

Answer 1

The sampling distribution of the sample mean is a probability distribution of all possible sample means of a given sample size that can be drawn from a population. The shape of the sampling distribution of the sample mean is approximately normal if the sample size is large enough (n > 30) regardless of the shape of the population distribution1. Therefore, we do not need to make any assumptions about the shape of the population1.

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Explanation: