Final answer:
To calculate the probability of more than 20 phone calls during peak time, one typically uses a Poisson distribution but cannot do so without further information such as the standard deviation. For the hospital research on post-op patients, the situation is a discrete probability distribution because the number of times a patient rings the nurse is a set of discrete whole numbers, and each has its associated probability.
Step-by-step explanation:
To determine the probability that employees make more than 20 long-distance phone calls during the peak time, we would use the Poisson distribution if the calls were random and independent events. However, as the question does not provide the standard deviation or the exact distribution type, we can't calculate the exact probability without additional information. Typically, for a Poisson distribution, we would calculate the probability of observing more than a certain number of events (calls) given an average rate (20 calls) using the Poisson probability function. Although we can't conduct the exact calculation here, we understand that the probability of observing exactly 20 calls is different from observing more than 20.
In the case of the hospital researcher interested in the number of times patients ring the nurse, we have a discrete probability distribution because it describes the probability of occurrence of discrete outcomes (0, 1, 2, 3, 4, 5 times a patient rings the nurse). It is 'discrete' because the number of rings can only take on certain values (whole numbers in this case), and 'probability distribution' because each outcome has a distinct probability associated with it.