QUESTION 5: 1.) An inspector selects seven parts (without replacement) 'om each batch of parts produced by a production line; the batch fails inspection if at least one of these seven parts is defective. (a) Compute the probability that a batch fails when it contains 80 parts, of which ve are defective. {b} Compute the probabilityr that a batch does not fail inspection when it contains 45 parts, of which six are defective. (c) Consider the batch 'om part (a). Compute the mean and variance of the number of non-defective parts among those parts selected by the inspector. {(1} Consider the batch 'om part (a). Suppose the inspector will select I parts for inspection (not necessarily seven; the batch fails if at least one of these 1 parts is defective). Find the smallest value of t that will cause this batch to fail inspection with probability 0.60 or higher