![]() A z-score of 0 indicates that the given point is identical to the mean. Convert Z-score to Percentile This ONLY applies to Refer to. A z-table, also known as a standard normal table or unit normal table, is a table that consists of standardized values that are used to determine the probability that a given statistic is below, above, or between the standard normal distribution. 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). Isabella’s z-score is: (20-22)/5 -0.4 Hannah’s z-score is: (33-38)/12.5 -0.4 So they’re equally young in their degree level. 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. ![]() To determine the critical region for a normal distribution, we use the table for the. ![]() ![]() \( \newcommand\), that is the shaded area on the left side. In a right-tailed test with 0.01, the critical value of z is. ![]()
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