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A Quality Analyst Wants to Construct a Sample Mean Chart

question 105

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A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:  Weight (ounces)   Day  Monday 23222324 Tuesday 23211921 Wednesday 20192021 Thursday 18192019 Friday 18202220\begin{array} { r } { \text { Weight (ounces) } }\\\begin{array} { l l l l l } \text { Day } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\text { Tuesday } & 23 & 21 & 19 & 21 \\\text { Wednesday } & 20 & 19 & 20 & 21 \\\text { Thursday } & 18 & 19 & 20 & 19 \\\text { Friday } & 18 & 20 & 22 & 20\end{array}\end{array} If he uses upper and lower control limits of 22 and 18 ounces, on what day(s) , if any, does this process appear to be out of control?

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