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 8.2 minutes and a standard deviation of 2.9minutes. 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 33 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 33 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 33 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) here for 33 jetsexpected total mean time =8.2*33=270.6

and std deviation =2.9*(33)1/2 =16.6592

probability that for 33 jets on a given runway, total taxi and takeoff time will be less than 320 minutes

=P(X<320)=P(Z<(320-270.6)/16.6592)=P(Z<2.9653)=0.9985

b)

P(X>275)=1-P(X<275)=1-P(Z<(275-270.6)/16.6592)=1*P(Z<0.2641)=1-0.6042 =0.3958

c)

P(275<X<320)=P(0.2641<Z<2.9653) =0.9985-0.6042 =0.3943

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