We encountered the central limit theorem in the previous chapter when we took samples from a uniform distribution and averaged them. In fact, the central limit theorem works for any distribution of values, provided the distribution has a finite standard deviation.
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The central limit theorem states that the distribution of sample means will be normally distributed irrespective of the distribution from which they were calculated.
It doesn't matter that the underlying distribution is exponential—the central limit theorem shows that the mean of random samples taken from any distribution will closely approximate a normal distribution. Let's plot a normal curve over our histogram to see how closely it matches.
To plot a normal curve over our histogram, we have to plot our histogram as a density histogram. This plots the proportion of all the points that have been put in each bucket rather than the frequency. We can then overlay the normal probability density with the...