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

The average September rainfall in Erie, Pennsylvania, is a random variable X with mean μ = 102 mm.
Assume that the amount of rainfall is normally distributed with standard deviation σ = 48.
(a) Express P(128 ≤ X ≤ 150) in terms of F(z) and compute its value numerically.
(b) Let P be the probability that September rainfall will be at least 120 mm. Express P as an integral of an appropriate density function and compute its value numerically.