The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with parameter μ = 50. (Round your answers to four decimal places.) (a) Calculate the approximate probability that between 35 and 90 tickets are given out on a particular day. (b) Calculate the approximate probability that the total number of tickets given out during a 5-day week is between 215 and 285. (c) Use software to obtain the exact probabilities in (a) and (b) and compare to their approximations. Calculate the exact probability that between 35 and 90 tickets are given out on a particular day. Calculate the exact probability that the total number of tickets given out during a 5-day week is between 215 and 285.

A manufacturer has determined that a machine averages one faulty unit for every 500 it produces. What is the probability that an order of 300 units will have one or more faulty units?

What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.