Question

An automaker does quality control tests on the paint thickness at different points on its car parts since there is some variability in the painting process. A certain part has a target thickness of 2mm. The distribution of thicknesses on this part is skewed to the right with a mean of 2mm and a standard deviation of 0.5 mm. A quality control check on this part involves taking a random sample of 100 points. i) What is the shape of the sampling distribution of the sample mean thickness? Explain your answer. ii) Assuming the stated mean and standard deviation of the thicknesses are correct, what is the probability that the mean thickness in the sample of 100 points is between 1.9 mm and 2.1 mm? Interpret your finding.

          An automaker does quality control tests on the paint thickness at different points on its car parts since there is some variability in the painting process. A certain part has a target thickness of 2mm. The distribution of thicknesses on this part is skewed to the right with a mean of 2mm and a standard deviation of 0.5 mm. A quality control check on this part involves taking a random sample of 100 points. i) What is the shape of the sampling distribution of the sample mean thickness? Explain your answer. ii) Assuming the stated mean and standard deviation of the thicknesses are correct, what is the probability that the mean thickness in the sample of 100 points is between 1.9 mm and 2.1 mm? Interpret your finding.

An automaker does quality control tests on the paint thickness at different points on its car parts since there is some variability in the painting process. A certain part has a target thickness of 2mm. The distribution of thicknesses on this part is skewed to the right with a mean of 2mm and a standard deviation of 0.5 mm. A quality control check on this part involves taking a random sample of 100 points. i) What is the shape of the sampling distribution of the sample mean thickness? Explain your answer. ii) Assuming the stated mean and standard deviation of the thicknesses are correct, what is the probability that the mean thickness in the sample of 100 points is between 1.9 mm and 2.1 mm? Interpret your finding.

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