Probability

1. In semi-conductor manufacturing process, the maximum number of defects that we can accept on a wafer is 5. If the number of defects on a circuit follows a Poisson distribution with a mean of 2, 

a. What is the probability that we reject a circuit? write the formula, write the value of each parameter (e.g. lambda), then provide the final value (no need to show the calculation steps; if you correctly write the value of parameters in the beginning you can only list the final value).

b. What percentage of circuits will be rejected in each lot? in each day? In each week?

c. On average, how many acceptable wafers do we make before we make an unacceptable wafer?

d. Imagine we can purchase a better machine that produces an average of 1 defect per wafer. Using the new machine, what percentage of each production batch will be unacceptable?

e. If the machine costs $1M and each unacceptable product costs us $200. At what level of production, would the investment in the new machine pay-off? How should the managers decide whether they should purchase the machine or not?