The manager of a large manufacturing company wants to estimate the proportion of items that have been manufactured with defects. How many items are required for a random sample to obtain a margin of error of at most 0.04 with 90% confidence?

Assume that there is a 11% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?