6. A company that buys batteries in very large batches from a supplier decides to intro-duce a quality control scheme. If the proportion of defective batteries in one of theselarge batches is 20%a) what is the probability of accepting the batch if the quality control scheme is toaccept a batch only if a random sample of size 10 contains at most 1 defective.b) Approximate the probability of accepting the batch if the scheme is to accept abatch only if a random sample of size 150 has at most 12 defectives.7. A discrete random variableXhas the following probability distribution:X0123p(X)0.3450.4410.1890.025a) Find the mean and standard deviation ofX.b) Find the probability thatXis equal to 0 if it is known thatXis less than 2.c) Find the probability thatXis greater that 2.5.d) If a random sample of 100 observations ofX, whereXhas the above distribution,is obtained, what is the approximate probability that the sample mean is greater than1?e) If a random sample of 10 observations is taken from the above distribution, wouldthe method you used in (b) still be valid? Why or why not?arrive8. The “Loan over the phone” desk in a bank has found that calls for loans arrive randomlyand independently at an average rate of 25 per 5-day week of 8 hour days.a) If the cost of processing each call is $2.00, what is the expected cost of processingorders in any given week?What is the variance of the processing cost in any givenweek?b) What is the probability of at least 2 calls for loans in any given day?