Let X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes. If the random variable X is known to be exponentially distributed, what is the probability that the wait time is greater than 37 minutes

Probability that the wait time is greater than 37 minutes is 0.3474.

Step-by-step explanation:

We are given that the random variable X is known to be exponentially distributed and X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes.

Let X = waiting time for a car to pass by on a country road

The probability distribution function of exponential distribution is given by;

    where, = parameter of distribution.

Now, the mean of exponential distribution is =  which is given to us as 35 minutes that means    .

So, X ~ Exp(  )

Also, we know that Cumulative distribution function (CDF) of Exponential distribution is given as;

 , x > 0

Now, Probability that the wait time is greater than 37 minutes is given by = P(X > 37 min) = 1 - P(X 37 min)

  P(X 37 min) =        {Using CDF}

                         = 1 - 0.3474 = 0.6525

So, P(X > 37 min) = 1 - 0.6525 = 0.3474

Therefore, probability that the wait time is greater than 37 minutes is 0.3474.

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step-by-step explanation: