Calculating areas with sample means

So far we have calculated the probabilities of observations using mean and standard deviation values from the population. However, we can also calculate these observation probabilities using mean and standard deviation values from the sample. For instance, we could have a question along the lines of what is the probability that the sample mean of the beard length of 50 Scandinavian hipsters is larger or equal to 26 millimeters. Because in this example we are talking about a specific sample from the population, we make use of the sampling distribution and not the population distribution.

Because we make use of the sampling distribution, we are now using the standard deviation of the sampling distribution which is calculated using the formula \(\sigma / \sqrt{n}\).

Calculate the probability that a sample mean of the beard length of 50 Scandinavian hipsters is larger or equal to 26 millimeters. Recall that the population is contained in the variable scandinavia_data. Take all the steps indicated by comments in the editor.

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Calculating areas with sample means

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