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1. 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 16. Let X represent the number of components checked by an inspector in a shift. Then the total number checked is 5X, which has mean 600 and standard deviation 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.

The calculation for the mean is OK, but the calculation of the standard deviation is not. Remember that a standard deviation is a square root, and that:

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We need to do our algebra on the variance, not the standard deviation. Therefore:

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2. It is estimated that in normal highway driving, the number of miles that can be covered by automobiles of a particular model on 1 gallon of gasoline can be represented by a random variable with mean 28 and standard deviation 2.4. Sixteen of these cars, each with 1 gallon of gasoline, are driven independently under highway conditions. Find the mean and standard deviation of the average number of miles that will be achieved by these cars.

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3. A process is known to produce bricks whose weights are

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