A milk processing plant takes regular samples during production and tests them for microbial contamination. Unfortunately the test is not completely reliable: even if there is no contamination, the test will give a positive result on average once for every hundred tests. Type your answers here (a) Suppose that 20 samples are tested from one batch. Assuming that there is really no contamination in the batch, what is the probability distribution of the number of positive results obtained? What assumption(s) must be made? (b) For the situation in (a), what is the probability that at least one one sample gives a positive test result? (c) A particular batch of unknown quality has been tested as described, and three of the 20 tests were positive. State, with supporting calculations, what you would conclude about this batch.