Cue Stick Cliff Summey is the quality control assurance engi

“Cue Stick” Cliff Summey is the quality control assurance engineer for Sticks and Stones Billiard Supply, a manufacturer of billiard supplies. One of the items that Sticks and Stones produces is sets of pocket billiard balls. Cliff has been monitoring the finish of the pocket billiard balls. He is concerned that sets of billiard balls have been shipped with an increasing number of scratches. The company’s goal is to have no more than an average of one scratch per set of pocket billiard balls. A set contains 16 billiard balls. Over the last week, Cliff selected a sample of 48 billiard balls and inspected them to determine the number of scratches. The data collected by Cliff is below.

Ball   Scratches
1 0
2 0
3 1
4 0
5 0
6 3
7 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 1
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 1
35 0
36 0
37 0
38 0
39 0
40 0
41 0
42 1
43 0
44 0
45 1
46 0
47 0
48 0

a) What type of probability distribution would be used to analyze this situation?
b) How many scratches are in the sample? a) What type of probability distribution would be used to analyze this situation?

c) What would be the average number of scratches for 48 pocket billiard balls (three sets) if Sticks and Stones has met its goal?

d) What is the probability that a random sample would have at least as many scratches as occurred in the sample Cliff took?

e) Based on the sample evidence, does it appear the Sticks and Stones is meeting its goal and why or why not?

Solution