College students with checking accounts typically write relatively few checks in any giv...

College students with checking accounts typically write relatively few checks in any given month, whereas nonstudent residents 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 nonstudent residents. 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 probability 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 average 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. Referring to Part (b), what is the approximate probability that is at most 20? at least 25?