A quality control manager at an auto plant measures the paint thickness on newly painted cars. A certain part that they paint has a mean thickness of 2mm with a standard deviation of 0.8mm.
The manager takes a daily random sample of thickness measurements from 100 randomly chosen points on these parts and calculates the sample mean thickness
-x from each sample. We can assume that the points in each sample are independent.
What will be the shape of the sampling distribution of -x?
Even though we don't know the shape of the population distribution of thicknesses, the sampling distribution of -x will be approximately normal since the sample size is large (n=100≥30).
