Crunchy Corn Chips are packaged in bags labeled net weight 10 ounces. In fact, the weight of

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Question:

Crunchy Corn Chips are packaged in bags labeled “net weight 10 ounces.” In fact, the weight of a bag of Crunchy Corn Chips follows a normal distribution with mean ounces and standard deviation ounces.

(a) Suppose that the manufacturers of Crunchy Corn Chips adjust their filling machines to dispense an average of 10.4 ounces per bag. Experience has shown that 0.26 ounces for this process. What percentage of the bags will weigh less than advertised?

(b) Worried about customer complaints and potential lawsuits, the manufacturers decide that no more than 0.5% of bags of Crunchy Corn Chips should be underweight. There are two possible adjustments that can be made: change the mean setting on the filling machines while leaving the standard deviation constant, or leave the mean at 10.4 ounces and try to adjust the standard deviation. Describe the necessary adjustments under each of these two plans. Which do you think is more feasible? Explain.

(c) The manufacturers have also discovered that if they put too many chips in a bag, the bag will burst. In order to balance their concerns over customer satisfaction and possible breakage, management wants to adjust the filling machines so that only 0.5% of bags are underweight and only 2% of bags weigh more than 10.5 ounces. Find the values of and that accomplish these goals.