Question

After completing a study, Orlando International Airport managers concluded that the time needed to get passengers loaded on an airplane is normally distributed with a mean equal to 22.5 minutes and a standard deviation equal to 5.25 minutes. Recently one airplane required 33 minutes to get passengers on board and ready for takeoff. Find the probability that a flight will take 33 or more minutes to get passengers loaded.

Answer 1

Probability = 0.0228

Explanation:

Let X be a random variable which is a measure of the time to get a passenger on board.

Mean(u) = 22.5mins

Standard deviation (s) = 5.25mins

X = 33mins

From Pr(X>33), starting from Pr(X = 33)

For normal distribution, Z = 7(X - u) /s

Z= (33 -22.5) /5.25

= 10.5/5.25

= 2

From the normal distribution table, 2 = 0.4772

Recall that

If Z is positive,

Pr(x>a) = 0.5 - table value

Pr(x<a) = 0.5 + table value

Therefore;

Pr(X>33) = 0.5 - 04772

= 0.0228