A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 25 minutes.
a. How large a sample should she take to estimate the mean time to within 2 minute with 90% confidence?
b. How large a sample should she take to estimate the mean time to within 2 minute with 99% confidence?