Suppose that arrival times for an elevator in a large hotel are bell-shaped with a mean of 20 seconds and a standard deviation of 6 seconds.

Question

 What percent of time will the elevator arrive between 2 seconds and 8 seconds?

Answer 1

x = arrival time, N(20,6)

want to find P(2 < x < 8)

convert inequality to standard normal using standardized variable:

z = (x - mean)/SD

P(2 < x < 8) = ((2-20)/6) < z < (8-20)/6)) = P(-3 < z < -2) = P(z < -2) - P(z < -3) = 0.0228 - 0.0013 = 0.0215

converted to percentage = 2.15%