Q1: To construct an x - chart and an R - chart for a process, you have collected 10 samples from the process outputs with 7 observations in each sample and found that the average of the sample means is 20 and the average of the sample ranges is 2. What should be the upper control limit of the R-chart? (Answer with 3 decimal places eg. 10.123)

Q2: Consider a manufacturer that produces a cereal product. A cereal box is acceptable by the customer if its weight is between 15.8 and 16.2 Suppose that the firm collects a large number of cereal boxes from its manufacturing process and finds that their average weight is 15.9 ounces with a standard deviation of 0.2 ounces. What is the proces capability index of this process? (Answer 3 decimal places eg 0.123)

Q3: Suppose you have collected 16 samples, where each sample has 131 items, and that the total number of defectives in the collected data is 45. What is the sample size (n)?

Q4: Suppose you have collected 15 samples, where each sample has 100 items. If the total number of defectives in the collected data is 5, what is the average of sample proportions? (Answer with 4 decimal places eg. 0.1234)

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