The administration of a large university wants to take a random sample to measure student opinion of a new food service on campus. It plans to use a continuous scale from 1 to 100, on which 1 is complete dissatisfaction and 100 is complete satisfaction.
The administration knows from past experience with such questions that the standard deviation for the responses is going to be about 5, but it does not know what to expect for the mean.
It wants to be almost sure that the sample mean is within plus or minus 1 point of the true population mean value. How large will the random sample have to be?