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Answer: "B" is the correct response.

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Marty’s record suggests that the pattern of incompetence established by his two predecessors continues in his tenure at Natural Butter. He was correct in his speculation about the plus and minus three units, but these represent the standard deviation rather than the average range

The book section that Marty Graw skipped describes a method for estimating the standard deviation. This estimation method became especially useful in the 1930s, before electronic calculators and computers were available to calculate the standard deviation. The formula for estimating the standard deviation is:

is, of course, taken from the control chart, while is a weighting value that will give an estimate of the standard deviation when divided into . The value of varies, depending on the sample size used in the control chart.

Returning to Marty's example, n=5, and is 4.652, so the estimated standard deviation would be:

Another piece of misinformation that Marty applied was that of the scaling. For a normal distribution, 99.73% of the area under the curve will be included by moving plus and minus three standard deviations (not three R-bars). Since the standard deviation for this example is 2, the right tail should come down at about 16:

Right tail

Left tail

The chart that Marty should have drawn follows:

Next month, we will continue to search for the capability of this system.