![]() ![]() 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). If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If the area is not in the table, use the entry closest to the area. 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). Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. In Sals example, the z-score of the data point is -0.59, meaning the point is approximately 0.59 standard deviations, or 1 unit, below the mean, which we can. ![]() So if the standard deviation of the data set is 1.69, a z-score of 1 would mean that the data point is 1.69 units above the mean. 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. A 1 in a z-score means 1 standard deviation, not 1 unit. 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. ![]()
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