A control chart for a bottled product requires that a sample consisting of a sin

Question

A control chart for a bottled product requires that a sample consisting of a single bottle contain between 350 and 360 milliliters of product. Sample data, taken when the bottling process was in control, indicate that bottles contain an average of 355 milliliters, and you know that the bottling process has a standard deviation of 4 milliliters when in control. Given that the bottling process is in control, what portion of its output will fall outside the limits of the chart?

100%

21.12%

4.56%

39.44%

1.24%

100%

21.12%

4.56%

39.44%

1.24%

Explanation / Answer

= 355 = 4

P(350 < x < 360)

= P((350 - 355) / 4 < z < (360 - 355) / 4)

= P(-1.25 < z < 1.25)

Using z tables, the value is

0.8944 - 0.1056

= 0.7888

The probability that a value falls outside the range

=1 - 0.7888

= 0.2112

= 21.12%.

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