3. (TCO B) DCW Chemical is planning to implement an acceptance sampling plan for raw materials. A random sample of 22 batches from a large shipment (having a large number of batches) is selected. If two or more of the 22 batches fail to meet specifications, then the entire shipment is returned. Otherwise, the shipment is accepted. In a sample of 22 batches from a population that is 1% defective (1% of the batches fail to meet specifications), find the probability that a. two or more batches fail to meet specifications. b. exactly two batches fail to meet specifications. c. fewer than two batches fail to meet specifications. (Points : 18) 4. (TCO B) The end-of-month cash flow for a company can be modeled by a normal distribution with a mean of $10,000 and a standard deviation of $7,000. Note that a positive cash flow figure means that there is a surplus of cash, but a negative cash flow means that we have a cash shortage. a. Find the probability that the end-of-month cash flow will be between $15,000 and $25,000. b. Find the probability that the end-of-month cash flow will be at least $5,000. c. The treasurer is concerned about the possibility of a cash shortage and wishes to develop strategies to manage cash flow. The treasurer wants to establish a reserve fund that can be used in case of negative cash flow. Suppose that the treasurer wants to be able to have a fund large enough to cover all but 1% of the months. How much money should be in the reserve fund? (Points : 18) 5. (TCO C) A survey is taken of U.S. companies that do business with firms in India. One of the questions in the survey was: Approximately how many years has your company been trading with firms in India? A random sample of 44 responses to this question yields the following results. Sample Size = 44 Sample Mean = 10.46 years Sample Standard Deviation = 7.7 years a. Compute the 95% confidence interval for the population mean number of years of trading with firms in India. b. Interpret this interval. c. How many firms should be sampled if we wish to generate a 95% confidence interval for the mean number of years of trading with firms in India that is accurate to within 1 year? (Points : 18) 7. (TCO D) A manager at Travis Savings and Loan believes that less than 52% of their depositors own their homes. A random sample of 100 depositors is selected with the results that 46 depositors own their homes and the other 54 do not own their homes. Does the sample data provide evidence to conclude that less than 52% of all depositors at Travis Savings and Loan own their homes (with a = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that less than 52% of all depositors at Travis Savings and Loan own their homes (with a = .05)? (Points : 24)