On a particularly busy section of the Garden State Parkway in New Jersey, police
ID: 3433487 • Letter: O
Question
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.)
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.
Explanation / Answer
(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