Homework: week '10 [homework Question 5, 5-3-71-T HW Score: 85%" 6'3 of8 > points assign B} Poisson distribution, Part 1 0M 0 Points: 0 DH Cliff is the qualityassurance engineer for a particular manufacturer of billiard supplies. One of the items that the manufacturer produces is sets of pocket billiard balls. Cliff has been monitoring the nish of the pocket billiard balls. He is concemed 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 two scratches per set of pocket billiard balls. Aset 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 accompanying data table. Complete parts a through d below. a Click on the icon to View the data table. a. Determine the number of scratches in the sample. The number of scratches in the sample is :l. Cliff is the quality-assurance engineer for a particular manufacturer of billiard supplies. One of the items that the manufacturer 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 accompanying data table. Complete parts a through d below. If Click on the icon to view the data table a. Determine the number of scratches in the sample. The number of scratches in the sample is 2. b. Calculate the average number of scratches for 48 pocket billiard balls if the manufacturer has met its goal. The average is 3. c. Determine the probability that there would be at least as many scratches observed per set of pocket billiard balls if the manufacturer has met its goal. The probability is 0.8009. d. Based on the sample evidence, does it appear that the manufacturer has met its goal? Provide statistical reasons for the conclusion. Consider an event with a probability less than 0.05 unlikely. The probability that Cliff would observe at least as many scratches as he did if the company's goal had been met is greater than 0.05. So it cannot be determined that the manufacturer's goal has likely not been met