Question

Asked Nov 8, 2019

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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.

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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