A city librarian claims that books have been checked out an average of seven (or more) times

Question:

A city librarian claims that books have been checked out an average of seven (or more) times in the last year. You suspect he has exaggerated the checkout rate (book usage) and that the mean number of checkouts per book per year is, in fact, less than seven. Using the computerized card catalog, you randomly select one book and find that it has been checked out four times in the last year. Assume that the standard deviation of the number of checkouts per book per year is approximately 1.
a. If the mean number of checkouts per book per year really is 7, what is the z -score corresponding to four?
b. Considering your answer to part a , do you have reason to believe that the librarian’s claim is incorrect?
c. If you knew that the of the number of checkouts was mound shaped, would your answer to part b change? Explain.
d. If the standard deviation of the number of checkouts per book per year were 2 (instead of 1), would your answers to parts b and c change? Explain.
Distribution
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