The exponential distribution is frequently applied to the waiting times between successes in a poisson process. if the number of calls received per hour by a telephone answering service is a poisson random variable with parameter Î" = 6, we know that the time, in hours, between successive calls has an exponential distribution with parameter Î² = 1/6. what is the probability of waiting more than 15 minutes between any two successive calls?

Question

Mathematics

Grimes

10 November, 09:25

The exponential distribution is frequently applied to the waiting times between successes in a poisson process. if the number of calls received per hour by a telephone answering service is a poisson random variable with parameter Î" = 6, we know that the time, in hours, between successive calls has an exponential distribution with parameter Î² = 1/6. what is the probability of waiting more than 15 minutes between any two successive calls?

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Dickens · Answer 1

P (x>15) = 0.9656

Step-by-step explanation:

No. of calls received is a poisson random variable with parameter = 6

mean = 6

And the waiting time between the phone calls received is exponentially distributed with parameter m = 1/6.

We need to find the waiting time more than 15 minutes.

1hour = 60 minutes

15 minutes = 0.214 hours.

P (x>x) = e^{-mx)

P (x>0.214) = e^{-0.214/6}

= 0.9656