question 5

According to the records of a soft drink company, the bottles for their onelitersized products contain an average (mean) of 1.02 liters of beverage, with a standard deviation of 0.16 liters. As part of routine quality assurance, a sample of 70 bottles has been taken. The sample mean amount of beverage in these 70 bottles was 0.982 liters. Assuming the company's records are correct, find the probability of observing a sample mean of 0.982 liters or less in a sample of 70 bottles. Can}.r your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. A brokerage surveyr reports that 39% of all individual investors have used a discount broker (one that does not charge the full commission). If a random sample of 140 individual investors is taken, approximate the probability that fewer than 53 have used a discount broker. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) [D x b 9 The Diversity, Equity, and Inclusion (DEI) office of a major multinational bank is investigating the process used to make recent hires for financial analysts. The office knows that exactly 12% of all applications were from minority candidates and that exactly 10% of the open positions were filled by members of a minority. For the investigation, the DEI office will take a random sample of 1650 applications. Let p be the proportion of minority applicants in the sample. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. X ? (b) Find the standard deviation of p. (c) Compute an approximation for P (p