Final answer:
To determine the probability that in a randomly selected hour the number of calls is three, 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. The probability is approximately 0.1804.
Step-by-step explanation:
To determine the probability that in a randomly selected hour the number of calls is three, 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.
We can use the formula for the probability mass function of the Poisson distribution to calculate the probability:
P(X=k) = (e^-λ * λ^k) / k!
Where X is the random variable representing the number of calls, k is the desired number of calls (in this case, three), and λ is the average rate of calls per hour (two).
Substituting the values into the formula, we have:
P(X=3) = (e^-2 * 2^3) / 3!
Simplifying, we get:
P(X=3) = (e^-2 * 8) / 6
Rounding to four decimal places, the probability that in a randomly selected hour the number of calls is three is approximately 0.1804.