![]() ![]() And, because we know that z-scores are really just standard deviations, this means that it is very unlikely (probability of \(5\%\)) to get a score that is almost two standard deviations away from the mean (\(-1.96\) below the mean or 1.96 above the mean). Thus, there is a 5% chance of randomly getting a value more extreme than \(z = -1.96\) or \(z = 1.96\) (this particular value and region will become incredibly important later). We can also find the total probabilities of a score being in the two shaded regions by simply adding the areas together to get 0.0500. What did we just learn? That the shaded areas for the same z-score (negative or positive) are the same p-value, the same probability. ![]() ![]() \( \newcommand\), that is the shaded area on the left side. We say the data is 'normally distributed': The Normal Distribution has: mean median mode symmetry about the center 50 of values less than the mean and 50 greater than the mean Quincunx You can see a normal distribution being created by random chance It is called the Quincunx and it is an amazing machine. ![]()
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