# Question

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. P(0 < z < 1.2)

ii. P(0 < z < 2.5)

iii. P(z > .8)

iv. P(z < 1.0)

b. Find the exact probabilities in part.

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

a. Use Shah’s approximation to find

i. P(0 < z < 1.2)

ii. P(0 < z < 2.5)

iii. P(z > .8)

iv. P(z < 1.0)

b. Find the exact probabilities in part.

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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