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 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.)

Answer 1

expected time for 33 jets =33*8.3=273.9

and standard deviation for 33 jets =3.5*sqrt(33)=20.1060

a)

for normal distribution z score =(X-μ)/σx

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

probability =P(X<320)=(Z<(320-273.9)/20.106)=P(Z<2.29)=0.9890

b)

probability =P(X>275)=P(Z>(275-273.9)/20.106)=P(Z>0.05)=1-P(Z<0.05)=1-0.5199=0.4801

c)

probability =P(275<X<320)=P((275-273.9)/20.106)<Z<(320-273.9)/20.106)=P(0.05<Z<2.29)=0.989-0.5199=0.4691