Question

At a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 190 calls and a standard deviation of 10 calls. What is the probability that during a given hour of the day there will be more than 192 calls, to the nearest thousandth?

Answer 1

Let X ~ N(190, 10^2). Compute Z = (192 − 190)/10 = 0.2.
P(X > 192) = P(Z > 0.2) = 1 − Φ(0.2) ≈ 1 − 0.57926 = 0.42074 ≈ 0.421 (to the nearest thousandth).