A plant manager is interested in developing a quality-control program for an assembly line that produces light bulbs. To do so, the manager considers the quality of the products that come from the line. The light bulbs are packed in boxes of 12, and the line produces several thousand boxes of bulbs per day. To develop baseline data, some of the workers test all the bulbs in 100 boxes. They obtain the following results:
|
No. of Defective Bulbs/Box
0
|
No. of Boxes
8
|
|
1
|
27
|
|
2
|
3
|
|
3
|
2
|
a. Plot a histogram of these results.
b. What kind of theoretical distribution might fit this situation well? Explain.
c. Estimate parameters for the distribution you chose in part b by calculating the sample mean and variance. Use the theoretical distribution with its estimated parameters to estimate P(0 Defective), P(l Defective), P(2 Defective), and P(3 Defective). How do these estimates compare to the relative frequency of these events in the data?