Boxes of Honey Nut Oatmeal are produced to contain 16.0 ounces, with a standard deviation of 0.20 ounce. For a sample size of 49, the 3-sigma -x chart control limits are

Upper Control Limit (UCL-x) = ounces
Lower Control Limit =(LCL=max

Explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weigths for the Boces of Honey Nut meal of a population, and for this case we know the distribution for X is given by:

Where and

Since the distribution for X is normal, we know that the distribution for the sample mean is given by:

And using the 3 sigma rule we can find the interval like this:

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