A quality engineer is monitoring a lens coating process, where a lens is either a high quality lens or not a high quality lens, and the monitoring process meets the conditions for a binomial experiment. The probability a lens is a high quality lens, in the monitoring process, is 0.92, based on relative frequencies.
a) If the quality engineer tests lenses until he/she finds 3 lenses that are not a high quality lens, what is the probability the quality engineer tests exactly 21 lenses?
b) If the quality engineer tests lenses until he/she finds 3 lenses that are not a high quality lens, what is the expected number of lenses that the quality engineer tests?
c) If the quality engineer tests lenses until he/she finds 3 lenses that are not a high quality lens, what is the standard deviation of the number of lenses that the quality engineer tests?