Everyone is familiar with waiting lines. We wait in lines at banks, groceries, and fast-food restaurants. There are also waiting lines in firms where trucks wait to load and unload and on assembly lines where stations wait for new parts. Management scientists have developed mathematical models that allow managers to determine the operating characteristics of waiting lines. The Poisson probability distribution is used extensively in waiting-line (or, queuing) models. Many models assume that the arrival of units for service is Poisson distributed with a specific value of u.

When the mean number of users of an automatic banking machine per 5- minute interval is 1.5, find the probability of the following events.

1. No users in the next 5 minutes.
2. Five or fewer users in the next 15 minutes.
3. Three or more users in the next 10 minutes.