SECTION 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 239 You can use the following guidelines to find various types of areas under the standard normal curve. Finding Areas Under the Standard Normal Curve 1. Sketch the standard normal curve and shade the appropriate area under the curve. 2. Find the area by following the directions for each case shown. a. To find the area to the left of z, find the area that corresponds to z in the Standard Normal Table. z 1.23 0 Use the table to find the area for the z-score. 1. The area to the left of z = 1.23 is 0.8907. 2. b. To find the area to the right of z, use the Standard Normal Table to find the area that corresponds to z. Then subtract the area from 1. z 1.23 0 Use the table to find the area for the z-score. 1. Subtract to find the area to the right of z = 1.23: 1 − 0.8907 = 0.1093. 3. The area to the left of z = 1.23 is 0.8907. 2. c. To find the area between two z@scores, find the area corresponding to each z@score in the Standard Normal Table. Then subtract the smaller area from the larger area. z 1.23 −0.75 Subtract to find the area of the region between the two z-scores: 0.8907 − 0.2266 = 0.6641. The area to the left of z = −0.75 is 0.2266. Use the table to find the areas for the z-scores. 0 1. 3. 4. The area to the left of z = 1.23 is 0.8907. 2. GUIDELINES Tech Tip You can use technology to find the area under the standard normal curve. For instance, you can use the ShadeNorm feature on a TI-84 Plus to graph the area under the standard normal curve between z = -0.75 and z = 1.23, as shown below. The area between the two z-scores is shown below the graph. (Note that when you use technology, your answers may differ slightly from those found using the Standard Normal Table.) Area=.664024 low=-.75 up=1.23
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