Five inspectors are employed to check the quality of components produced on an assembly line. For each inspector the number of components that can be checked in a shift can be represented by a random variable with mean 120 and standard deviation 15. Let X represent the number of components checked by an inspector in a shift. Then the total number checked is 5X, which has a mean of 600 and a standard deviation of 80. What is wrong with this argument? Assuming that inspectors' performances are independent of one another, find the mean and standard deviation of the total number of components checked in a shift.
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