A sampling distribution is a distribution based around a sample statistic, such as x-bar. We would much rather use the information from the population (mu) instead, but sometimes that information is not available or sometimes it is too hard/not possible to sample an entire population. So, we use a sampling distribution instead.
The main question then becomes: if we take a sample from the population, what is the probability that the sample statistic (x-bar) is actually representative of the population statistic (mu)? In other words, are the sample and population close enough to one another that they are essentially the same? That depends. To find out, we need a sample mean, a population mean, a population standard deviation, and n, which is the number of observations in the sample. Plug these values into the z-score formula
z = (x-bar - u)/(sigma/rad(n)). (Awkward writing the formula in the blog without all of the math symbols!)
This will give you the z-score. Then, plug this value into Normalcdf, and this will give you the probability that our sample represents the population. Note: if your x-bar is higher than mu, do 1-Normalcdf instead.
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