The taxi and takeoff time for commercial jets is a random variable x with a mean

Question

The taxi and takeoff time for commercial jets is a random variable x with a mean 8.3 minutes and a standard deviation of 2.4 of 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 35 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 35 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 35 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

Explanation / Answer

a) for 35 jets mean =35*8.3 =290.5

std error =2.4*(35)1/2 =14.20

P(X<320)=P(Z<(320-290.5)/14.20)=P(Z<2.0777)=0.9811

b)P(X>275)=1-P(X<275)=1-P(Z<-1.0917)=1-0.1375=0.8625

c)P(275<X<320)=0.9811-0.1375=0.8436

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