The manufacturer of silicon wafers used in integrated circuits requires the removal of contaminating particles of a certain size. This process rinses batches of 20 wafers with deionized water. Personnel count the number of contaminating particles. The counts are wel modeled by a Poisson distribution with a rate of six particles per wafer. Consider a randomly selected wafer:
a) Find the probability that this wafer has at least one particle
b) Find the probability that this wafer has exactly six particles
c) Find the expected number of particles, the varience, and the standard deviation