Normal curve approximation. A. K. Shah published a simple approximation for areas under the normal curve in The American Statistician (Feb. 1985). Shah showed that the area A under the standard normal curve between 0 and z is

a. Use Shah’s approximation to find i. P10 6 z 6 1.22 ii. P10 6 z 6 2.52 iii. P1z 7 .82 iv. P1z 6 1.02

b. Find the exact probabilities in part a.

c. Shah showed that the approximation has a maximum absolute error of .0052. Verify this for the approximations in part a.

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- z(4.4 z)/10 for 0 Z 2.2 A .49 .50 for 2.2 < < 2.6 for z 2.6