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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 λ = 6, we know that the time, in hours, between successive calls has an exponential distribution with parameter β =1/6. what is the probability of waiting more than 15 minutes between any two successive calls?

Respuesta :

Answer:

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

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