Ingots are huge pieces of metal, often weighing in excess of 10,000 kilograms, made in a giant mold. They must be cast in one large piece for use in fabricating large structural components for automobiles and planes. If they crack while being made, the crack may propagate into the section required for the component, compromising its structural integrity. Airplace manufacturers insist that metal for their planes be defect-free, so the ingot must be melted and remade if any cracking is detected.

Even though the metal from a defective ingot is recycled, the cost of scrapping and re-working can run into tens of thousands of dollars. Metal manufacturers would like to avoid cracking if at all possible. But the casting process is complicated, and not everything can be controlled completely. At various casting operations, the percentage of ingots which are free of cracks ranges from 75% to 85%.

The attached Excel file contains information about one particular casting operation which has been assigned to you to analyze.Enter your 9-digit student numberinto the highlighted cell in the attached Excel file, which will be used to determine your assigned operation.

METAL INGOT CASTING OPERATIONS 12702.xlsx

QUESTION 1(a): SAMPLING DISTRIBUTION(3 POINTS)

In the Excel file, you are provided data on the typical percentage of all ingots manufactured at your assigned operation which are cracked. During the first month of your assignment, you randomly select a batch of ingots. What is the probability that this batch will have less than the indicated percentage (in Excel) which are cracked?

QUESTION 1(b): CONFIDENCE INTERVAL (5 POINTS)

At the beginning of the second month, you randomly select another batch of ingots, and count how many of them are cracked. You want to find a confidence interval for the percentage of all ingots manufactured that month which will be cracked.

QUESTION 1(c): HYPOTHESIS TEST (5 POINTS)

In an attempt to reduce the number of cracked ingots, the engineers and chemists at your location made changes to the casting process. During the third month, you randomly select another batch of ingots, and count how many of them are cracked. Based on the results on this third batch, compared to the typical level of cracked ingots indicated in part 1(a), would you conclude that the changes were successful or not?

QUESTION 2: CONFIDENCE INTERVAL (5 POINTS)

In your fourth month, you are asked to also take a look at impurity levels in ingots. You randomly select a fourth batch of ingots, and work with the chemists to determine impurity levels measured in ppm (parts per million). Based on these results, you want to estimate, to a certain degree of confidence, what the mean level of impurities will be for all ingots manufactured that month.

REQUIREMENTS FOR ALL QUESTIONS:

Draw a picture.Your solution for each part of each question must include a picture showing what you are trying to solve.

Show your work.You must show all intermediate steps, calculations, and values used to arrive at your final answer for each question.

State your conclusion.You must include a briefconcluding sentence answering each question.

• Be clear.The overall clarity, neatness, and completeness of your answers will be considered during marking, including the use of proper spelling and grammar.