The final example of this section explains the origin of the proportions given in the Empirical Rule. We can see from the first line of the table that the area to the left of \(-5.22\) must be so close to \(0\) that to four decimal places it rounds to \(0.0000\). Thus, if we know the area to the right is. Normal tables, computers, and calculators provide or calculate the probability P ( X < x ). This area is represented by the probability P ( X < x ). The z table shows the area to the left of various z-scores. This table can replace or supplement Table 1 in the Aron, Aron and Coups, 6th Ed. The shaded area in the following graph indicates the area to the left of x. Find the z-score that has 37.83 of the distribution’s area to the right. Similarly, here we can read directly from the table that the area under the density curve and to the left of \(2.15\) is \(0.9842\), but \(-5.22\) is too far to the left on the number line to be in the table. Example 2: Find Z-Score Given Area to the Right.We can see from the last row of numbers in the table that the area to the left of \(4.16\) must be so close to 1 that to four decimal places it rounds to \(1.0000\). We obtain the value \(0.8708\) for the area of the region under the density curve to left of \(1.13\) without any problem, but when we go to look up the number \(4.16\) in the table, it is not there. Standard Normal Distribution Table (Right-Tail Probabilities) z. \) by looking up the numbers \(1.13\) and \(4.16\) in the table.
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