Find the probability

Question

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.

 

(b) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Use 3 decimal places.)

 

(c) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Use 3 decimal places.)

 

Answer 1

Sample mean = 275/33 = 8.33. To exceed 275 minutes, each jet on average will need to take more than 8.33 minutes

(8.33-8.3) / (3.5/sqrt(33)) = .03 / .6092 = .0492

p(Z > .092) ~ .4801

There is a 48% probability that the takeoff time for 33 jets will exceed 275 minutes.

Give the other one a go and let me know if you have questions!