Question: Cliff Summey is the quality-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 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 are displayed in the file called Poolball.
a. Determine the number of scratches in the sample.
b. Calculate the average number of scratches for 48 pocket billiard balls if Sticks and Stones has met its goal.
c. Determine the probability that there would be at least as many scratches observed per set of pocket billiard balls if Sticks and Stones has met its goal.
d. Based on the sample evidence, does it appear that Sticks and Stones has met its goal? Provide statistical reasons for your conclusion.