On a particular busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeding drivers. Assume the time that elapses between successive speeders is exponentially distributed with the mean of 30 minutes. What is the probability of a waiting time in excess of 40 minutes between successive speeders?Multiple Choice0.88600.26360.34210.8083

The problem describes an exponential distribution. The exponential distribution has a probability density function (PDF) given by:

f(x|λ) = λ * exp(-λx) for x >= 0, 0 otherwise

Where λ = 1/(mean of the distribution)

In this case, the mean is given as 30 minutes, so λ = 1/30.

The question asks for the probability that the waiting time exceeds 40 minutes. This is equivalent to finding the survival function at 40 minutes, which is 1 minus the cumulative distribution function (CDF) at 40 minutes.

The CDF of an exponential distribution is given by:

F(x|λ) = 1 - exp(-λx)

So, the survival function is given by:

S(x|λ) = exp(-λx)

Substituting λ = 1/30 and x = 40 into the survival function gives:

S(40|1/30) = exp(-(1/30)*40)

Calculating this gives approximately 0.4493. However, this is not one of the options given in the multiple choice question. It seems there may be an error in the question or the provided answer choices.

The problem describes an exponential distribution. The exponential distribution has a probability density function (PDF) given by:

f(x|λ) = λ * exp(-λx) for x >= 0, 0 otherwise

Where λ = 1/(mean of the distribution)

In this case, the mean time between speeders is given as 30 minutes, so λ = 1/30.

The question asks for the probability that the waiting time exceeds 40 minutes. This is a survival function, which is 1 minus the cumulative distribution function (CDF). For an exponential distribution, the CDF is:

F(x|λ) = 1 - exp(-λx) for x >= 0, 0 otherwise

So the survival function S(x|λ) = exp(-λx)

Substituting λ = 1/30 and x = 40 into the survival function gives:

S(40|1/30) = exp(-(1/30)*40)

Calculating this gives approximately 0.4493. However, this is not one of the options given in the multiple choice question. It seems there may be an error in the question or the provided answer choices.