Question

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.7 minutes and a standard deviation of 2.6 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.)

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	8.7
std deviation   =σ=	2.6000
sample size       =n=	35
std error=σx̅=σ/√n=	0.4395

probability that for 35 jets on a given runway, total taxi and takeoff time will be less than 320 minutes

=P(average time will be less than 320/35 =9.143 minutes)

probability =

P(X<9.143)

=

P(Z<1.01)=

0.8438

b)

probability =

P(X>7.857)

=

P(Z>-1.92)=

1-P(Z<-1.92)=

1-0.0274=

0.9726

c)

probability =

P(7.857<X<9.1423)

=

P(-1.92<Z<1.01)=

0.8438-0.0274=

0.8164