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 bank’s accounts are held by students and that 50% are held by people who are not college students. Let x denote the number of checks written in a given month by a randomly selected bank customer.
a. Give a sketch of what the population distribution of x might look like.
b. Suppose that the mean value of x is 22.0 and that the standard deviation is 16.5. If a random sample of n = 100 customers is to be selected and  denotes the sample mean number of checks written during a particular month, where is the sampling distribution of  centered, and what is the standard deviation of the  distribution? Sketch a rough picture of the sampling distribution.
c. What is the approximate probability that  is at most 20? At least 25?