An auto-maker 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 2 mm. The distribution of thicknesses on this part is skewed to the right with a mean 2 mm and a standard deviation of 0.5 mm. A quality control check on this part involves taking a random sample of 100 points and calculating the mean thickness of those points. 1. What is the shape of the sampling distribution of the sample mean thickness? 2. Find the mean and standard deviation of the sampling distribution the mean of the sample mean the standard deviation of the sample mean 3. Assuming the stated mean and standard deviation of the thicknesses are correct, what is the approximate probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value?