By default, the pct_change Series method calculates the percentage change between the current element and previous element. This transforms the raw stock closing prices into daily percentage returns. The first element of the returned Series is a missing value as there is no previous price.

Histograms are fantastic plots to summarize and visualize one-dimensional numeric data. It is clear from the plot that the distribution is symmetrical but it remains difficult to determine whether it is normal or not. There are formal statistical procedures to determine the normality of a distribution but we will simply find how close the data matches the 68-95-99.7 rule.

Step 5 calculates the number of standard deviations away from the mean for each observation which is referred to as the z-score. This step uses the methods and not the symbols (- and /) to do subtraction and division. The method for less than is also used in favor of the symbols in step 6.

It may seem odd that the mean is being taken in step 6. The result of the abs_z_score.lt(1) expression is a Series of booleans. As booleans evaluate to 0 or 1, taking the mean of this Series returns the percentage of elements that are True, which is what we desired.

We can now more easily determine the normality of the returns by comparing the resulting numbers (78.7-95.7-98.5) to the 68-95-99.7 rule. The percentages deviate greatly from the rule for 1 and 3 standard deviations, and we can conclude that Amazon daily stock returns do not follow a normal distribution.