Managers at a service center design studies aimed at estimating the population average time (= ) in minutes spent by customer service representatives per one call. They assume that the individual duration is normally distributed with population standard deviation, = 12 minutes.

1. Assuming that the margin of error for an interval should not exceed 5 minutes, find the SMALLEST sample size required for a 99% confidence interval.

2. Determine the SMALLEST sample size needed for the 90% confidence interval that should be NO WIDER than 6 minutes.

3. Determine the width of a 95% interval based on a sample of 100 records