suppose that college students with a checking account typically write relatively few checks in any given month whereas people who are not college students typically write many more checks during a month. suppose that 50% of a banks account are held by students and that 50% are held by people who are not college students. let X represent the number of checks written in a given month by a randomly selected bank customer. suppose that the mean of X is 22.0 and that the standard deviation is 16.7. if a random sample of n+ 100 customers is to be selected and X denotes the sample mean number of checks written during a particular month where is the sampling distribution of X centered? what is the standard deviation of the sampling distribution of X? what is the approximate probability that X is at 20? what is the approximate probability that X is at least 25?