![]() 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). The point where the row & column meets for the corresponding z-score value is the critical value of Z or the rejection area of one or two tailed z-distribution. Refer the column & row values for z-score. 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). Z-scores generally ranges from -3.99 to 0 on the left side and 0 to 3.99 on the right side of 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. >Standard Normal Distribution Z Table for students. gives a probability that a statistic is between 0 (mean) and Z. ![]() 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. where X is a score from the original normal distribution, is the mean of the original normal distribution, and is the standard deviation of original normal distribution. ![]() \( \newcommand\), that is the shaded area on the left side. ![]()
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