The ABC Manufacturing Corp. has been having trouble with one of its machines. Out of all of the parts the machine produces, 23% are defective. An inspector selects a group of 12 parts at random from the machines output. Express your answers to four decimal places. Express the probabilities as decimal fractions not as percentages.
a) What is the probability that exactly two of these parts will be defective?
b) What is the probability that none of these parts will be defective?
c) What is the mean of the number of defective parts among the group of parts selected?
d) What is the variance of the number of defective parts among the group?