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.

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

Answer 1

We have modelled together the take off and taxi times for the jets.

We have been asked in the questions about the probability of the total time of a number of jets. Hence, we need the distribution of the sum of the times. Using the central limit theorem we have

We have 37 jets therefore n = 37

z-score = z-score = (x- E(X)) / (S(X)

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)

P(< 320 ) = P( Z < 0.61)

.....................using normal distribution tables

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)

P(> 275) = P( Z > -1.51)

= P( Z < 1.51)

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

P( 275 < <320) = P( < 320) - P( < 275)

= P(Z < 0.61) - P(Z < -1.51)

= P( Z < 0.61) - [1 - P( Z < 1.51)]

Using the probabilities from above we have