The time required to pass through security screening at the airport can be annoying to travelers. The mean wait time during peak periods at Cincinnati/Northern Kentucky International Airport is 12.1 minutes (The Cincinnati Enquirer, February 2, 2006). Assume the time to pass through security screening follows an exponential distribution.
It's is 8:00 am (a peak period) and you just entered the security line. To catch your place, you must be at the gate within 30 minutes.
If it takes 12 minutes from the time you clear security until you reach your gate, what is the probability you will miss your flight (to 3 decimals)?