A passenger metal detector at Chicago\'s Midway Airport gives an alarm 0.33 time

Question

A passenger metal detector at Chicago's Midway Airport gives an alarm 0.33 time 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 89th percentile waiting time until the next alarm. (Round your intermediate calculations and answer to 4 decimal places.)

A passenger metal detector at Chicago's Midway Airport gives an alarm 0.33 time a minute.

Explanation / Answer

(a) P ( X < t ) = 0.5
so P ( X > t ) = 0.5 = e^ t .
Solve for t using = 0.33: 0.5 = e (0.33) t ,

ln(0.5) = ln[ e (0.33) t ],
0.6931 = (0.33) t ,
t = 0.6931/0.33
=2.1003 minutes

b) P ( X < t ) = 0.25 so
P ( X > t ) = 0.75 = e t .
Solve for t using = 0.33:
0.75 = e (0.33) t ,
ln(0.75) = ln[ e (0.33) t ],
0.2877 = (0.33) t ,
t = 0.2877/0.33
= 0.8718 minutes

(c) P ( X < t ) = 0.89 so
P ( X > t ) = 0.11 = e t .
Solve for t using = 0.33:
0.11 = e (0.33) t ,
ln(0.11) = ln[ e (0.33) t ],
2.2072 = (0.33) t ,
t = 2.2072/0.33
=6.6884 minutes

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