Question: The administration of a large university wants to use a random sample of students to measure student opinion of a new food service on campus. Administrators plan to use a continuous scale from 1 to 100, where 1 is complete dissatisfaction and 100 is complete satisfaction. They know from past experience with such questions that the standard deviation for the responses is going to be about 5, but they do not know what to expect for the mean. They want to be almost sure that the sample mean is within plus or minus 1 point of the true population mean value. How large will their random sample have to be?