Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, m.

Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, m. The managers plan to choose a random sample of completion times and estimate m via the sample. Assuming that the standard deviation of the population of completion times is 10.1 minutes, what is the minimum sample size needed for the managers to be 99% confident that their estimate is within 2.2 minutes of m ?