A passenger metal detector at Chicago\'s Midway Airport gives an alarm 0.40 time

Question

A passenger metal detector at Chicago's Midway Airport gives an alarm 0.40 time a minute. (a) Find the median waiting time until the next alarm. (Round your intermediate calculations and answer to 4 decimal places.) Median waiting time minutes (b) Find the first quartile of waiting time before the next alarm. (Round your intermediate calculations and answer to 4 decimal places.) First quartile of waiting time minutes (c) Find the 75th percentile waiting time until the next alarm. (Round your intermediate calculations and answer to 4 decimal places.) 75th percentile waiting time minutes

Explanation / Answer

Solution:

From the given information

= 0.40

therfore, P(X > x) = e-x = e-0.40x

a) To find x such that

P(X > x) = 0.5

=> e-0.40x = 0.5

=>-0.40x = ln(0.5)

=> x = (-1/0.40) ln(0.5)

=> 1.7328

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b) To find x such that

P(X x) = 0.25

=> P(X >x) = 0.75

=> x = (-1/0.40) ln(0.75)

= 0.7192

----------------------------------------

c) To find x such that

P(X x) = 0.75

=> P(X >x) = 0.25

=> x = (-1/0.40) ln(0.25)

= 3.4657

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