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Describe the distribution of sample means (i.e., shape, measure of central tendency, and variability) for samples...

Describe the distribution of sample means (i.e., shape, measure of central tendency, and variability) for samples of size n = 49 selected from a population with mean µ = 14 and standard deviation σ = 7. Be specific and calculate as necessary.
Math   Statistics-And-Probability   
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Answer #1

Let X be the random variable.

The sample size is

As per the central limit theorem, when the sample size is large (i.e. greater than 30), the distribution of the sample means is approximately normal with mean, and variance, .

The aim is to find the sampling distribution for the random variable .

As per the given information, and the description above, follows the normal distribution with parameters:

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