APPENDIX A Alternative Presentation of the Standard Normal Distribution A5 Finding Area Under the Standard Normal Curve Find the area under the standard normal curve to the left of z = -0.99. SOLUTION The area under the standard normal curve to the left of z = -0.99 is shown. −0.99 z 0 Area = 0.3389 Area = 0.5 − 0.3389 From the Standard Normal Table (0-to-z), the area corresponding to z = -0.99 is 0.3389. Because the area to the left of z = 0 is 0.5, the area to the left of z = -0.99 is Area = 0.5 - 0.3389 = 0.1611. You can use technology to find the area to the left of z = -0.99, as shown at the left. TRY IT YOURSELF 2 Find the area under the standard normal curve to the left of z = 2.13. Answer: Page A43 Finding Area Under the Standard Normal Curve Find the area under the standard normal curve to the right of z = 1.06. SOLUTION The area under the standard normal curve to the right of z = 1.06 is shown. 1.06 z 0 Area = 0.3554 Area = 0.5 − 0.3554 From the Standard Normal Table (0-to-z), the area corresponding to z = 1.06 is 0.3554. Because the area to the right of z = 0 is 0.5, the area to the right of z = 1.06 is Area = 0.5 - 0.3554 = 0.1446. You can use technology to find the area to the right of z = 1.06, as shown at the left. TRY IT YOURSELF 3 Find the area under the standard normal curve to the right of z = -2.16. Answer: Page A43 EXAMPLE 2 EXAMPLE 3 TI-84 PLUS 0.5–normalcdf(0,0.99) 0.1610870617 TI-84 PLUS 0.5–normalcdf(0,1.06) 0.1445723279
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