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 \[0.04\,\text{mm}\] with a standard deviation of \[0.003\,\text{mm}\]. 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: \[\sigma_{\bar{x}_1-\bar{x}_2}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_\text{2}^2}{n_2}}\] Why is it not appropriate to use this formula for the standard deviation of \[\bar{x}_\text{A}-\bar{x}_\text{B}\]? Choose 1 answer: