I forgot to add another quick, much shorter question, An inspector selects eight parts (without replacement) from each batch of parts produced by a production line; the batch

fails inspection if at least one of these eight parts is defective.

(a) Compute the probability that a batch fails when it contains 90 parts, of which six are defective.

(b) Compute the probability that a batch does not fail inspection when it contains 54 parts, of which nine are

defective.

(c) Consider the batch from part (a). Compute the mean and variance of the number of non-defective parts among

those parts selected by the inspector.

(d) Consider the batch from part (a). Suppose the inspector will select t parts for inspection (not necessarily eight; the

batch still fails if at least one of these t parts is defective). Find the smallest value of t that will cause this batch to

fail inspection with probability 0.50 or higher. (I AM ONLY LOOKING FOR AN ANSWER FOR PART D)