What is the percentages of time will the elevator arrive in more than 8 seconds and

Question

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.

Please help I don't understand this question

(d) What percent of the time will the elevator arrive in more than 8 seconds?

Answer 1

x = mean arrival time. x is normally distributed with mean of 20 and standard deviation (SD) of 6: N(20,6)

We need to find probability x > 8, then convert that probability to percentage (multiply by 100).

need to standardize x to z-statistic which is N(0,1) to determine probability:

z = (x - mean)/SD, so for x = 8, mean = 20 and SD = 6:

P(x > 8) = P(z > (8-20)/6) = P(z > -2) = 1 - P(z < -2) = 1 - 0.0228 = 0.9772