When circuit boards used in the manufacture of compact disc players are tested, the long run percentage of defectives is 5%. Let X= the number of defective boards in random sample of size n=25, so X ~ Bin( 25, .05).
a) Find the probability that the number of defective boards is (i) At most 2 (ii) At least 5 (iii) Between 1 and 4, inclusive.
b) What is the probability that none of the 25 boards is defective? c) Calculate the expected value and standard deviation of X.