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 2.9 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 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)


(b) What is the probability that for 36 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 36 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

This is a normal distribution question with

Sample size (n) = 36
Since we know that

a) P(x < 8.89)=? (320/36)
The z-score at x = 8.89 is,

z = 1.2208
This implies that
P(x < 8.89) = P(z < 1.2208) = 0.8889
b) P(x > 7.64)=?
The z-score at x = 7.64 is,

z = -1.3656
This implies that
P(x > 7.64) = P(z > -1.3656) = 1 - 0.0860
P(x > 7.64) = 0.914
c) P(7.64 < x < 8.89)=?

This implies that
P(7.64 < x < 8.89) = P(-1.3656 < z < 1.2208) = P(Z < 1.2208) - P(Z < -1.3656)
P(7.64 < x < 8.89) = 0.8889 - 0.0860
P(7.64 < x < 8.89) = 0.8029
PS: you have to refer z score table to find the final probabilities.
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