Suppose nonconforming parts are produced with a rate α = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).
(a) If x denotes the number of nonconforming parts made during one hour, what distribution does x follow? Please define the parameter(s) needed for defining the distribution based on the information provided.
(b) What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?
(c) What are the expected value and standard deviation of the number of nonconforming part produced during a 90-min period?
(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?