Question

When Zahra commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 28 minutes and a standard deviation of 4.5 minutes. What is the probability that on a given day, her commute will be longer than 38 minutes, to the nearest thousandth?

Answer 1

z = (38 − 28)/4.5 = 10/4.5 ≈ 2.222.
P(X > 38) = 1 − Φ(2.222) ≈ 0.013 (to the nearest thousandth).