When crossing the Golden Gate Bridge traveling into San Fran

When crossing the Golden Gate Bridge, traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time (in minutes) drivers wait in line to pay the toll follows an exponential distribution with a probability density function of f(x) = 0.17e^.17x.

What is the mean waiting time that drivers face when entering San Francisco via the Golden Gate Bridge? (Round your answer to 2 decimal places.)

What is the probability that a driver spends more than the average time to pay the toll? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

What is the probability that a driver spends more than 16 minutes to pay the toll? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

What is the probability that a driver spends between 2 and 7 minutes to pay the toll? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

Solution

a)

Mean waiting time = 1/lambda = 1/0.17 = 5.88 [answer]

****************

b)

Here,

F(x) = 1 - exp(-0.17x)

Thus,

P(x>5.88) = exp(-0.17*5.882352941) = 0.3679 [answer]

*******************

c)

P(x>16) = exp(-0.17*16) = 0.0659 [answer]

*****************

d)

P(2<x<7) = exp(-0.17*2) - exp(-0.17*7) = 0.4075 [ANSWER]