8.20 College students with checking accounts typically write relatively few checks in any given month, whereas adults who are not 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 adults who are not 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 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. A random sample of n 5 100 customers is to be selected. 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?