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 x denotes the sample average number of checks written during a particular month, where is the sampling distribution of x centered, and what is the standard deviation of the x distribution? Sketch a rough picture of the sampling distribution.
c. Referring to Part (b), what is the approximate probability that x is at most 20? at least 25?