Chapter 8.2, Problem 20E

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.

1. a. Make a sketch of what the probability distribution of x might look like.
2. b. Suppose that the mean value of x is 22.0 and that the standard deviation is 16.5. A random sample of n = 100 customers is to be selected. Where is the sampling distribution of $\bar{x}$ centered, and what is the standard deviation of the sampling distribution of $\bar{x}$？ Sketch a rough picture of the sampling distribution.
3. c. Referring to Part (b), what is the approximate probability that $\bar{x}$ is at most 20? at least 25?