The time required to pass through security screening at the airport can be annoying to travelers. The mean wait time during peak periods at Ohara International Airport is 12.3 minutes. Assume the time to pass through security screening follows an exponential distribution.

a) What is the probability it will take less than 10 minutes to pass through security screening during a peak period? Compute four decimal places

b) What is the probability it will take more than 20 minutes to pass through security screening during a peak period? Compute four decimal places

c) What is the probability it will take between 10 and 20 minutes to pass through security screening during a peak period? Compute four decimal places

d) It is 8:00 A.M. (a peak period) and you just entered the security line. To catch your plane 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? Compute four decimal places