One measure of physical fitness is the amount of time it takes for the pulse rate to return to normal after exercise.  A random sample of 100 people of a particular type exercised on stationary bicycles for 30 minutes.  The amount of time it took for their pulse rates to return to pre-exercise levels was measured and recorded.  If times are normally distributed with a standard deviation of 2.3 minutes, estimate with 99% confidence the true mean pulse rate recovery time for all people of this type.

The mean of the data is 15.00 minutes.  Assume that the standard deviation referred to above is that of all possible people of this type.

How large a random sample would be needed to achieve a confidence range of one-half minute with a 99% confidence?