We began this tutorial by drawing samples from a population that has a uniform distribution, calculating the mean of each set of scores, and plotting the values of the sample means. We saw that, even though the population distribution was completely flat, when we took an infinite number of successive random samples from this population, the distribution of those sample means became approximately normally distributed with mean µ and standard deviation σ/√N ( ~N(µ, σ/√N)) as the sample size (N) increased. The last component of the central limit theorem tells us that the sampling distribution of the mean will be approximately normally distributed no matter what the population distribution looks like.

Let's repeat this same process, drawing samples from a Poisson distribution and a normal distribution. Both types of distributions are often found in psychological research.

• A Poisson distribution is positively skewed and is often found when studying rare events (e.g., number of major life crises within a month interval).
  
  
• A normal distribution is unimodal, symmetric, and bell-shaped and describes a wide array of physical and psychological attributes.