# Requirements A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution?

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Requirements A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution?

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Step 1

Sampling distribution of the sample mean:

• If the true population distribution of a random variable, say, x, is normal with parameters, mean μ and standard deviation σ, then, whatever be the size (n) of the sample taken from the population, the distribution of the sample mean is also normal, with parameters, mean μ and standard deviation σ/√n.
• Even if the true population distribution of a random variable, say, x, is not normal and has population mean μ, standard deviation σ, then, for a large size (n ≥ 30) of a sample taken from the population, the di...

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