A container of car antifreeze is supposed to hold 3785mL of the liquid. Realizing that fluctuations are inevitable, the quality-control manager of the Taconic Chemical Company wants to be quite sure that the standard deviation is less than 30mL. Otherwise, some containers would overflow while others would not have enough of the coolant. She selects a simple random sample of 24 containers and finds that the mean is 3789mL and the standard deviation is 42.8mL. Use these sample results to construct the 99% confidence interval for the true value ofs. Does this confidence interval suggest that the variation is at an acceptable level?
Assume that each sample is a simple random sample obtained from a population with a normal distribution.