Problem:
In a manufacturing facility that produces laptop computers, there are three production lines that operate independently of each other. On one line, circuit boards on the way to final assembly that do not meet quality standards get "kicked" off the line into a holding "waste" bin at a rate of 6 per half-hour. Since the time between arrivals is random, an exponential distribution can be applied with respect to the time between arrivals.
Required:
Question 1) What is the probability the next circuit board that is kicked to the waste bin will occur in 3 minutes or more, 6 minutes or more, or 12 minutes or more?
Question 2) Conversely, what is the probability that the next defective board will occur in 3 minutes or less, 6 minutes or less, or 12 minutes or less?
Question 3) Since arrivals into the waste bin are random, if we want to determine the probability of a specific number of defective circuit boards in a specific time, we can apply the Poisson distribution. What is the probability that exactly 8 circuit boards get kicked to the bin in a 35 minute interval?
Solve the given numerical problem and illustrate step by step calculation.