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    Normal Distribution for Pacific Fishing Company

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    Pacific Fishing Company is a fish packing company. The company sells cans of salmon with a labeled weight of 213 grams. The quality control engineer reports that the cans actually have a mean weight of 218 grams and a standard deviation of 5 grams. The weights are approximately normally distributed.
    a. What percentage of cans will have less than 210 grams of salmon?
    b. What percentage of cans will have more than 228 grams of salmon?
    c. Consumer legislation states that no more than 10% of cans may contain less than the labeled weight. Is Pacific Fishing in compliance with the law?
    d. In order to ensure compliance with the law the company has decided to increase the amount of salmon it puts in each can. What average amount of salmon per can would ensure compliance with the law?
    e. The company has been approached by a salesman selling a new canning machine that would significantly reduce the standard deviation of the canning process. If the company wanted to maintain the same mean weight (218 grams), what is the largest standard deviation they could accept and still be in compliance?

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    We have an approximately normal distribution with μ=218 grams and σ=5 grams
    P(X<210)=P(z<(210-218)/5)=P(z<-1.60)≈0.0548 or ...

    Solution Summary

    This solution contains step-by-step calculations to determine the probability of certain scenarios in the Pacific Fishing Company.