College students with a checking account typically write

Chapter 0, Problem 8.20

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College students with a checking account 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 banks 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?