A passenger metal detector at Chicagos Midway Airport gives

A passenger metal detector at Chicago\'s Midway Airport gives an alarm 0.87 times a minute.

Find the median waiting time until the next alarm. (Round your intermediate calculations and answer to 4 decimal places.)

Find the first quartile of waiting time before the next alarm. (Round your intermediate calculations and answer to 4 decimal places.)

Find the 52th percentile waiting time until the next alarm. (Round your intermediate calculations and answer to 4 decimal places.)

Solution

The metal detector has 0.87 as lemda

Mean = 1/0.87 = 1.1494

Median of exponential distribution = ln2/0.87 = 0.7967

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I quartile = ln(4/3)/lemda = 0.3306

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52nd percentile = p where p is such that -ln(1-p)/0.87 = 0.52

-ln(1-p) = 0.4524

0.6361 = 1-p

p = 1-0.6361 = 0.3639

52nd percentile =0.3639