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The number of requests for assistance received by a towing service is a Poisson process with rate

α = 10 per hour.

(a) Compute the probability that exactly fifteen requests are received during a particular 2-hour period. (Round your answer to three decimal places.)

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Final answer:

To compute the probability that exactly fifteen requests are received during a particular 2-hour period with a rate of 10 requests per hour, we can use the Poisson distribution.

Step-by-step explanation:

To compute the probability that exactly fifteen requests are received during a particular 2-hour period, we can use the Poisson distribution. The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this case, the rate is α = 10 requests per hour.

The probability mass function (PMF) for a Poisson distribution is given by:

P(X = k) = e^(-λ) * (λ^k) / k!

where X is the random variable representing the number of events, λ is the average rate, and k is the number of events we want to find the probability for.

For this problem, we want to find the probability that exactly fifteen requests are received during a 2-hour period. Since the rate is 10 requests per hour, the average rate λ for a 2-hour period is 20. Therefore, the probability can be calculated as:

P(X = 15) = e^(-20) * (20^15) / 15!

Calculating this expression will give us the desired probability.

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