292 Chapter 7 The Normal Distribution SUMMARY To find an area under the standard normal curve by using Table A.2: Step 1: Sketch a normal curve, label the z-score or scores, and shade in the area to be found. Step 2: Look up the area in Table A.2 corresponding to each z-score. Step 3: ∙ To find the area to the left of a z-score, use the area in Table A.2. ∙ To find the area to the right of a z-score, find the area to the left and subtract from 1. ∙ To find the area between two z-scores, find the area to the left of each, then subtract the smaller area from the larger area. Check Your Understanding 2. Use Table A.2 to find the area to the left of z = 0.25. 0.5987 3. Use Table A.2 to find the area to the right of z = 2.31. 0.0104 4. Use Table A.2 to find the area between z = −1.13 and z = 2.02. 0.8491 Answers are on page 299. Finding areas under the standard normal curve by using technology Areas under the standard normal curve can be found by using technology. Examples 7.5 and 7.6 illustrate the method. EXAMPLE 7.5 Find the area between two z-scores by using technology In Example 7.4, we found the area between z = −1.45 and z = 0.42. Find this area by using technology. Solution We present results from the TI-84 Plus calculator. The area is found by using the normalcdf command. We enter the left endpoint of the interval (−1.45), the right endpoint (0.42), the mean (0), and the standard deviation (1). Step-by-step instructions are given in the Using Technology section on page 295. The TI-84 Plus gives the area as .5892279372. Rounding to four decimal places gives 0.5892. EXAMPLE 7.6 Find the area to the right of a z-score by using technology In Example 7.3, we found the area to the right of z = −0.58. Find this area by using Explain It Again technology. 1E99: In Example 7.6, we want to find the area between −0.58 and infinity. Since we can’t enter a value of infinity into the calculator, we enter the very large number 1E99 instead. Solution We present output from the TI-84 Plus calculator. We use the normalcdf command. We enter the left endpoint of the interval (−0.58). Since there is no right endpoint, we enter 1E99, which represents the very large number that is written with a 1 followed by 99 zeros. Then we enter the mean (0) and the standard deviation (1). Step-by-step instructions are given in the Using Technology section on page 295.
navidi_monk_elementary_statistics_2e_ch7-9
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