The engineer in Problem 6 was having a busy day, so instead of testing 20 lenses per hour he simply tested lenses until a defective lens was found.

(a) What is the probability that the engineer tested fewer than four lenses?

(b) What is the expected number of lenses that the engineer would test using this procedure?

(c) Write up a proposal for a quality inspection plan based on testing until a defective is found. Include both a warning and a critical (i.e., stop production) limit for the inspection team. Hint: Base your limits on the minimal number of defect-free lenses that an inspector must find at each inspection. You may want to use a spreadsheet (or other such tool) to calculate a series of probabilities to help you in defining limits.