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Acme Farms produces a line of dairy products, including milk. Because of uncertainties in the filling process, the actual amount of milk which a filling machine pours into a pint carton is slightly variable. Normally, the milk carton is expected to be filled to 16 fluid ounces with standard deviation of .03 fluid ounces.

1. What is the chance that any single carton will be filled with between 15.97 and 15.99 ounces of milk?

2. What proportion of all cartons will be filled with more than 16.07 ounces?

3. What is the chance that any single carton will be filled with less than 15.95 ounces?

4. Of the 10,000 cartons filled in a single production lot, how many of them will be filled with between 15.98 and 16.02 ounces?

5. Ninety-six percent (96%) of all the cartons will be filled with up to how much milk?

6. Cartons in the lower 9% of the filling distribution are rejected by quality control. What is the minimum fill (in-ounces) allowed per carton before it is rejected?

ABC Paper Corporation manufacturers a special grade of laminated (plastic coated) paper. For the current process being used, the quality control staff has shown that, on average, a defect in the lamination can be expected in every 1.25 square feet of laminated paper.

7. A square foot of the product is randomly selected for inspection after the coating is applied. What is the chance that there are no defects in the coating in this area?

8. A square foot of the product is randomly selected for inspection after the coating process. What is the chance that there is at least one defect in this area?

9. What is the chance that in the next five square feet of laminated paper, exactly as many defects as expected will be found?

10. What is the chance that in the next five square feet of laminated paper, half as many defects will be found as expected?

By corporate policy, the coating process must be stopped if the coating process if it is more likely than not that there will be more than one defect in the coating in any two square feet of laminated paper. (In other words, the coating process is stopped if the chance of finding more than one defect in the coating in any two square feet of the laminated paper exceeds .50).

11. A. What is the probability of finding more than one defect in any two square feet of laminated paper? B. Does this particular paint shop meet the stated probability criterion so that it will be shut down? Pick either yes or no.

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