Question

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 40 minutes and a standard deviation of 2 minutes. What percentage of customers have to wait between 37 minutes and 40 minutes, to the nearest tenth?

Answer 1

Compute the z-score: z = (37 − 40)/2 = −1.5.
P(37 ≤ X ≤ 40) = P(−1.5 ≤ Z ≤ 0) = Φ(0) − Φ(−1.5) = 0.5 − 0.0668 ≈ 0.4332.

So about 43.3% of customers wait between 37 and 40 minutes (to the nearest tenth).