Section 7.2 Applications of the Normal Distribution 305 Check Your Understanding 7. A population has mean �� = 6.9 and standard deviation �� = 2.6. Find the value that has 80% of the population below it (in other words, the 80th percentile). 9.084 Tech: 9.088 8. A population has mean �� = 53 and standard deviation �� = 34. Find the value that has 35% of the population above it. 66.26 Tech: 66.10 Answers are on page 310. USING TECHNOLOGY TI-84 PLUS Finding areas under a normal curve The normalcdf command is used to calculate area under a normal curve. Step 1. Press 2nd, then VARS to access the DISTR menu. Select 2:normalcdf (Figure A). Step 2. Enter the left endpoint, comma, the right endpoint, comma, the mean, comma, and the standard deviation. ∙ When finding the area to the right of a given value, use 1E99 as the right endpoint. ∙ When finding the area to the left of a given value, use −1E99 as the left endpoint. Step 3. Press ENTER. Using the TI-84 PLUS Stat Wizards (see Appendix B for more information) Step 1. Press 2nd, then VARS to access the DISTR menu. Select 2:normalcdf (Figure A). Step 2. Enter the left endpoint in the lower field, the right endpoint in the upper field, the mean in the �� field, and the standard deviation in the �� field. ∙ When finding the area to the right of a given value, use 1E99 as the right endpoint. ∙ When finding the area to the left of a given value, use −1E99 as the left endpoint. Step 3. Select Paste and press ENTER to paste the command to the home screen. Press ENTER again to run the command. Figure B illustrates finding the area to the right of x = 280 with �� = 272 and �� = 9 (Example 7.13). Figure A Figure B Finding a normal value corresponding to a given area The invNorm command is used to calculate the z-score corresponding to an area to the left. Step 1. Press 2nd, then VARS to access the DISTR menu. Select 3:invNorm (Figure C). Step 2. Enter the area to the left of the desired normal value, comma, the mean, comma, and the standard deviation. Step 3. Press ENTER. Using the TI-84 PLUS Stat Wizards (see Appendix B for more information) Step 1. Press 2nd, then VARS to access the DISTR menu. Select 3:invNorm (Figure C). Step 2. Enter the area to the left of the desired z-score in the area field, the mean in the �� field, and the standard deviation in the �� field. Step 3. Select Paste and press ENTER to paste the command to the home screen. Press ENTER again to run the command. Figure D illustrates finding the normal value that has an area of 0.98 to its left, where �� = 100 and �� = 15 (Example 7.17). Figure C Figure D
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