Suppose that 20% of articles produced by a machine are defective, the defective occurring at random during the production process. use a gaussian approximation to approximate the following probabilities. (a) find the probability that, if a sample of 400 items is taken from the production, more than 100 will be defective. (b) for what value of k is the probability 0.95 that the number of defectives in a sample of 400 will lie within 40 + k?