Suppose that the number of sick days an employee at XYZ Company takes per year is normally distributed with mean 9 days and standard deviation of 2.5 days.

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Suppose that the number of sick days an employee at XYZ Company takes per year is normally distributed with mean 9 days and standard deviation of 2.5 days.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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a) What proportion of the employees are out fewer than 7.5 days? b) What proportion of the employees are out more than 8 days? c) What proportion of the employees are out between 8 days and 13 days? d) The CEO of the company decides to award the employees with the fewest absences by giving a financial award to the employees with the lowest 10% of absences. What is the largest number of absences that an employee could have and still get a monetary award? e) On the other hand, the employees with the highest 10% of absences will be required to visit the company doctor for a physical. What is the lowest number of absences that an employee must have and still be required to see the doctor? f) Suppose that a sample of 16 employees is selected at random from this company. What is the chance that the average of the 16 employees is above 8.75? Below 9.5?

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