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Mean and standard deviation of difference of sample means


A car manufacturer has two production plants in different cities. Every day, plant A produces 120 of a certain type of car, while plant B produces 80 of those cars. On average, all of these cars have a paint thickness of 0.04mm with a standard deviation of 0.003mm.
Every day, quality control experts take separate random samples of 10 cars from each plant and calculate the mean paint thickness for each sample. They then look at the difference between those sample means.
Consider the formula:
Why is it not appropriate to use this formula for the standard deviation of x¯Ax¯B?
Choose 1 answer: