![]() Recall that the standard normal table gives the area to the left of z -values and the entire area under. The area under the curve to the left of a z -value corresponds to the lower tail area. A lower tail area should be found since the test statistic, z 1.37, is negative. STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. A standard normal distribution table is utilized to determine the region under the bend (f(z)) to discover the probability of a specified range of 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). Use the standard normal table to find the lower tail area for z. 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.
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