# Describe the shape, expected value and standard error for the distribution of sample means for samples of n = 36 scores selected from a population with a mean of  = 80 and SD = 24.

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Describe the shape, expected value and standard error for the distribution of sample means for samples of n = 36 scores selected from a population with a mean of  = 80 and SD = 24.

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Step 1

Given data

n = 36

mean = 80

SD = 24

Points on 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 distribution of the sample mean is approximately normal, ...

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