3.23 lab: interstate highway numbers primary u. s. interstate highways are numbered 1-99. odd numbers (like the 5 or 95) go north/south, and evens (like the 10 or 90) go east/west. auxiliary highways are numbered 100-999, and service the primary highway indicated by the rightmost two digits. thus, the 405 services the 5, and the 290 services the 90. given a highway number, indicate whether it is a primary or auxiliary highway. if auxiliary, indicate what primary highway it serves. also indicate if the (primary) highway runs north/south or east/west. ex: if the input is: 90 the output is: the 90 is primary, going east/west. ex: if the input is: 290 the output is: the 290 is auxiliary, serving the 90, going east/west. ex: if the input is: 0 the output is: 0 is not a valid interstate highway number.

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?