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 140 calls and a standard deviation of 10 calls. What is the probability that during a given hour of the day there will be less than 157 calls, to the nearest thousandth?

Answer 1

Let X ~ N(140, 10^2). Compute z = (157 − 140)/10 = 1.7.
P(X < 157) = P(Z < 1.7) ≈ 0.95543 ≈ 0.955 (to the nearest thousandth).