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 \(0.0000\). 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. The std regular distribution, also called the zed-distribution, is a special normal distribution where the base your 0 and the standard derogation is 1.Because the z - table gives you only 'less than' probabilities, subtract P ( Z < 1. 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 \(1.0000\). Use the z-table to find where the row for 1.5 intersects with the column for 0.00, which is 0.9332. 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. \) by looking up the numbers \(1.13\) and \(4.16\) in the table.
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