Final answer:
To determine the probability that in a randomly selected hour, the number of calls is five, 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 of occurrence. In this case, the average rate of calls is two per hour. Using the Poisson distribution formula, we find that the probability is approximately 0.033.
Step-by-step explanation:
To determine the probability that in a randomly selected hour, the number of calls is five, 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 of occurrence. In this case, the average rate of calls is two per hour.
The formula for the Poisson distribution is:
P(x; λ) = (e^(-λ) * λ^x) / x!
where x is the number of events, λ is the average rate of events, and e is the base of the natural logarithm (approximately 2.71828).
Plugging in the values, we have:
P(5; 2) = (e^(-2) * 2^5) / 5!
Simplifying the expression, we get:
P(5; 2) = (0.1353 * 32) / 120
Calculating the result, we find:
P(5; 2) ≈ 0.033