There is no nice formula for the standard normal cdf , but several good approximations have been published in articles. The following is from “Approximations for Hand Calculators Using Small Integer Coefficients” (Mathematics of Computation, 1977: 214–222). For 0 , z # 5.5,

(z)

8F 8C The relative error of this approximation is less than .042%.

Use this to calculate approximations to the following probabilities, and compare whenever possible to the probabilities obtained from Appendix Table A.3.

a. b.

c. P(24 , Z , 4)

d. P(Z . 5)