text: mean is $20273 and stan. deviation is $4100.  for 100 colleges? what is the probability that the mean tuition of the sample is within $410 of the population mean? for samples of size 100, the sample mean is approximately normal with mean equal to the population mean (20273) and standard deviation equal to population sd / sqrt(n) = 4100/sqrt(100) = 410.  by the empirical rule, the probability that the sample is within $410 of the population mean, of in other words, 1 standard deviation away, is 68%.