The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. suppose the number of tickets written per day follows a poisson distribution with a mean of 6.4 tickets per day. find the probability that less than 6 tickets are written on a randomly selected day from this population.

(a) the number of tickets that is written most often is 6.5 tickets per day.
(b) if we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.
(c) half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
(d) the mean has no interpretation since 0.5 ticket can never be written.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?