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 3.5 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 30 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 30 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 30 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

Given, = 9, = 3.5

Let X be the total taxi and takeoff time.

Then

X ~ N( n
, n^{2})

= N(30 * 9 , 30 *3.5^{2})

= N(270 , 367.5)

For normal distribution,

P( X < x) = P( Z < x - mean / standard deviation)

a)

P( X < 320) = P( Z < 320 - 270 / sqrt(367.5) )

= P( Z < 2.6082)

= **0.9954**

b)

P( X > 275) = P( Z > 275 - 270 / sqrt(367.5) )

= P (Z > 0.2608)

= 1 - P( Z < 0.2608)

= 1 - 0.6029

= **0.3971**

c)

P(275 < X < 320) = P( X < 320) - P( X < 275)

= P(Z < 320 - 270 / sqrt(367.5) ) - P( Z < 275 - 270 / sqrt(367.5) )

= P( Z < 2.6082) - P( Z < 0.2608)

= 0.9954 - 0.6029

= **0.3926**

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