There is no nice formula for the standard normal cdf Φ(z) , but several good approximati...

There is no nice formula for the standard normal cdf Φ(z) , 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,?

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. P(Z ≥ 1)

b. P(Z < – 3)

c. P(–4 < z <4)

d.P(Z > 5)