On a particularly busy section of the Garden State Parkway i

On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 21 minutes.

What is the probability of a waiting time less than 11 minutes between successive speeders? (Round your answer to 4 decimal places.)

What is the probability of a waiting time in excess of 24 minutes between successive speeders?(Round your answer to 4 decimal places.)

Solution

(a) Rate parameter ? =1/21= 0.0476

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(b) F(X)=1-exp(-x/21) for x>0

So the probability of a waiting time less than 11 minutes between successive speeders is

P(X<11) = 1-exp(-11/21) =0.40774

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(c) So is the probability of a waiting time in excess of 24 minutes between successive speeders is

P(X>24) =1-P(X<24)

=1-(1-exp(-24/21))

=0.3189