Final answer:
To calculate the probability of exactly five type 1 calls in one hour, we would use the Poisson distribution formula. The required average rate of calls is missing, thus it's impossible to provide an accurate answer without this information.
Step-by-step explanation:
The student is asking for the probability that exactly five type 1 calls are made from a motel during a 1-hour period. To answer this, we would typically use the Poisson distribution, which is a probability distribution that is used to model the number of events within a fixed interval of time, given the average number of times the event occurs over that interval. However, to provide an exact answer, specific information about the average rate of type 1 calls at the motel is needed, which is not included in the provided details.
Without the rate (average number of type 1 calls per hour), we can't calculate the exact probability using the formula P(X=k) = (e-λ * λk) / k!, where λ is the average rate, k is the number of events (type 1 calls in this case), and e is the base of the natural logarithm (approximately 2.71828). Thus, we are unable to determine which of the provided options (0.007, 0.0071, 0.0072, 0.0073) is the correct probability.
However, if the average is given, the calculation would follow by plugging in the necessary values and solving for P(X=5).