Final answer:
The statement is true; when the service facility operates at a capacity of serving four customers per hour, it can handle demand approximately 76 percent of the time. In the remaining 24 percent of time, queues may form due to demand exceeding capacity. Queueing theory and probability distributions are useful for analyzing such situations.
Step-by-step explanation:
The statement that the service facility can handle the demand per hour approximately 76 percent of the time at a rate of 4 per hour is indeed true. This implies that in about 24 percent of the time, the demand per hour will exceed four customers, which could indeed lead to queues forming. This situation can be modeled using probability and queueing theory, which are branches of mathematics that deal with the analysis of random processes and service systems respectively.
For example, if we know that on average one customer arrives every two minutes, we can infer that it takes six minutes on average for three customers to arrive. This would be an application of understanding the arrival rate in a system.To find the probability that it takes more than five minutes for the next customer to arrive after one has just arrived, we would use the exponential distribution because arrival times in many queueing systems can often be modeled this way. If the customers' arrival is described by an exponential distribution, then the probability of the time between arrivals can be calculated using the formula associated with this distribution.True. From the given information, it has been calculated that the service facility can handle the demand per hour approximately 76 percent of the time at a rate of 4 customers per hour. This means that approximately 24 percent of the time, demand per hour will be greater than four customers, causing queues to develop. This indicates that there will be times when the facility will not be able to meet the demand and customers will have to wait in queues.