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 of 9 minutes and a standard deviation of 3.3 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.)

Explanation / Answer

for total time mean =36*9 =324

and std deviation =3.3*(36)1/2 =19.8

a) P(X<320) =P(Z<(320-324)/19.8)=P(Z<-0.2020)=0.42

b)P(X>275)=1-P(X<275) =1-P(Z<-2.4748)=1-0.0067=0.9933

c)P(275<X<320)=0.42-0.0067 =0.4133

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