Discuss the below:
Q1. A random sample of 100 light bulbs is selected. Sixty were found to burn for more than 1,000 hours. Develop a 90 percent confidence interval for the proportion of bulbs that will burn more than 1,000 hours.
Q2. A health maintenance organization (HMO) wants to estimate the mean length of a hospital stay. How large a sample of patient records is necessary if the HMO wants to be 99 percent confident of the estimate and wants the estimate to be within plus or minus 0.2 days? An earlier study showed the standard deviation of the length of stay to be 0.25 days.
Q3. A large bank believes that one-third of its checking customers have used at least one of the bank's other services during the past year. How large a sample is required to estimate the actual proportion within a range of plus and minus 0.04? Use the 98 percent level of confidence.