Currently, when you check the fill volume for bottles of liquid pain killer, you take the cap off the bottle and pour the contents into a measuring device that can measure the volume within + .001 fl.oz. (in effect you destroy one bottle of product each time you do this). Since you get a big bonus for suggestions that result in cost savings, you find out that the actual volume of pain killer in a bottle can be calculated from the weight of the pain killer in that bottle (something you remembered from chemistry). So, if you could just weigh the bottle of pain killer without taking the cap off, you would be able to save thousands of units of product each year. A bottle of pain killer is comprised of a glass bottle, a cap, and the actual pain killer inside the bottle. Therefore the weight of a bottle of pain killer (WB) is given by
WB = WGB + WC + WPK
where WGB ,WC , and WPK are the weights of the glass bottle, cap, and pain killer respectively.
Before today's production run, you go out to the warehouse where they store component parts and estimate the mean and standard deviation of the weight of the glass bottles to be 5.00 and 0.10 grams and the mean and standard deviation of the caps to be 0.40 and .02 grams from a very large sample of glass bottles and caps. After today's production run, you take a very large sample of bottles of pain killer (complete units containing a bottle, cap, and the pain killer) and estimate the mean weight and standard deviation to be 20.00 and .50 grams.
a. Based on the information above, estimate the mean and standard deviation of the weight of the pain killer in each bottle.