16 A factory prints designs onto T-shirts, They check the design quality of each batch of T-shirts. If a b the checks, all the T-shirts in the batch have to be discarded, which adds extra production costs of El The production manager states that 85% of batches pass the quality checks, | dow a) In one week, 25 independent batches of T-shirts are printed. Find the probability that every b passes the quality checks. Give your answer to 4 decimal places. The production manager sets a target of less than $500 for the extra production costs for the we b) What is the probability that this target will be exceeded? Give your answer to 4 decimal The production data shows that out of 50 batches of T-shirts, three batches failed the quality c) By assuming that the 50 batches are independent, carry out a hypothesis test at the 10% significance level to test whether there is evidence that the proportion of batches that pass the quality check is actually higher than the production manager states