F(z) denotes the cumulative normal distribution function. Refer to a calculator or computer algebra system to obtain values of F(z).

Use a graph to show that F(−z) = 1 − F(z) for all z. Then show that if p(x) is a normal density function with mean μ and standard deviation σ, then for all r ≥ 0,

Pu-ro X u + ro) = 2F(r) - 1