1. How does one calculate joint probability?

2. The probability of drawing a pink chip from a bowl of different colored chips is 0.35, the probability of drawing a blue chip is 0.46, the probability of drawing a green chip is 0.15, and the probability of drawing a purple chip is 0.04. What is the probability that a blue chip or a purple chip will be drawn?

3. A steady stream of product has a fraction defective of 0.03. What is the probability of obtaining 2 nonconforming in a sample of 20?

4. Use an example when explaining the difference between a common cause and a special cause. Is this true for all charts: p, c, u, X, and R?

5. At a local county fair, the officials would like to give a prize to 100 people selected at random from those attending the fair. As of the closing day, 12,500 people have attended the fair and completed the entry form for the prize. What is the probability that an individual who attended the fair and completed the entry form will win a prize?

6. If there are five different parts to be stocked but only three bins available, what is the number of permutations possible for five parts taken three at a time?

7. If a manufacturer is trying to put together a sample collection of her product and order is not important, how many combinations can be created with 15 items that will be placed in packages containing five items? If order is important, how many permutations can be created?

8. How would you determine that a process is under control? How is the interpretation of a p, u, or c chart different from that of an X and R chart?

9. An environmental engineer places monitors in a large number of streams to measure the amount of pollutants in the water. If the amount of pollution exceeds a certain level, the water is considered nonconforming. In the past, the proportion nonconforming has been 0.04. What is the probability that one of the fifteen samples taken per day will contain an excessive amount of pollutants?

10. A steady stream of newspapers is sampled at a rate of 6 per hour. The inspector checks the newspaper for printing legibility. If the first page of the paper is not clearly printed, the paper is recycled. Currently, the fraction nonconforming in the lot is 0.030. What is the probability that 2 of the 6 papers checked will be nonconforming.

11. A line produces leather jackets. Once each hour, a jacket is selected at random from those made during that hour. Small imperfections (missed stitches, zipper catch, buttons missing, and loose threads) are counted. Recent data show an average of eight imperfections (nonconformities) in each sample. Using the formulas for a c chart, calculate the control limits and centerline for this situation. If management wants a process capability of four nonconformities per sample, will this line be able to meet that requirement?

12. At Fruits and Such, a local frozen fruit concentrate manufacturer, frozen grape juice is packed in 12-ounce cardboard cans. These cans are formed on a machine by spinning them from preprinted cardboard stock and attaching two metal lids, one for the top and one for the bottom. After the filling operation, samples (n=100) of the production are taken hourly. Inspectors look for several things that would make the can defective: how well the strip for opening the can operates, whether there are proper crimps holding the lids to the cardboard tube, if the lids are poorly sealed, etc. Create and interpret an np chart for the following data.