Arco Manufacturing makes electronic pagers. As part of the company's quality efforts, the company wishes to estimate the mean number of days the pager is used before repair is needed. A pilot sample of 40 pagers indicates a sample standard deviation of 200 days. The company wishes its estimate to have a margin of error of no more than 50 days and the confidence level must be 95%.
a. Given this information, how many additional pagers should be sampled?
b. The pilot study was initiated because of the costs involved in sampling. Each sampled observation costs approximately $10 to obtain. Originally, it was thought that the population's standard deviation may be as large as 300. Determine the amount of money saved by obtaining the pilot sample.