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The term 'population mean' refers to the average of a set of values or measurements from an entire population. It is denoted by \( \mu \). The population mean is a measure of central tendency and provides an overall idea of where the center of the data lies.

For instance, in our exercise, the population mean \( \mu \) is given as 64. This means, on average, the values in the population cluster around 64. This is crucial because when we take samples from this population, their means will revolve around this population mean.

A key aspect to understand is that the population mean remains constant, even as we take different samples from the population. This stability forms the basis for why sampling distributions behave the way they do, and helps in making inferences about the population based on samples.

Sample size, denoted by \( n \), is the number of observations or data points selected from a population to form a sample. In our exercise, the sample size is 36. The sample size plays a critical role in the accuracy and reliability of statistical estimations.

The larger the sample size, the more accurately it tends to represent the population. This is because larger samples reduce the effect of outliers and unusual observations.

An important formula related to sample size in the context of the standard deviation of the sampling distribution is \( \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \). Here, the sample size directly affects the denominator, meaning larger samples will result in a smaller standard deviation for the sample mean, indicating more precise estimates.

Standard deviation, represented by \( \sigma \), measures the dispersion or spread of a set of values from the mean. In simpler terms, it tells us how much the data varies from the average. In our exercise, the population standard deviation is 18.

When dealing with sampling distributions, the standard deviation of the sample mean, denoted as \( \sigma_{\bar{x}} \), is especially important. It is calculated using the formula:
\( \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \).

Using our given values, we substitute \( \sigma = 18 \) and \( n = 36 \) into the formula:
\( \sigma_{\bar{x}} = \frac{18}{\sqrt{36}} = \frac{18}{6} = 3 \).

This result tells us that the sample mean's distribution has a standard deviation of 3, which is useful for understanding the spread of sample means around the population mean.