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In Statistics - How to find Upper-Lower Control Limits -Mean/std deviation?

The question I've been working on for the past few hours, and completely stumped on is:

'The upper and lower control limits of a process are 66 and 54. Samples of size 16 are used for the inspection process. Determine the mean as well as the standard deviation for this process.'

Does anyone know how to do this?? I'm so confused....

Any help would be greatly appreciated!

Thanks!!

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Too late for Mike, but for anyone else finding this on Google...

The UCL and LCL are defined as the mean plus, or minus (respectively), 3 times the standard deviation. Assuming the process conforms to a normal distribution, the mean must therefore lie exactly half way between the two.

So the mean = (54 + 66) / 2 = 120 / 2 = 60.

And, if the LCL and UCL are 6 standard deviations apart (3 below the mean, 3 above the mean) then 1 standard deviation must be (66 - 54) / 6 = 12 / 6 = 2.

If the process is genuinely producing items to a normal distribution this means that 68% of the production will be within one standard deviation of the mean, i.e. between 60-2 and 60+2 (between 58 and 62). Three standard deviations covers 99.7% of your production. See http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

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PS: Clearly "reverse engineering" these result is cheating slightly - we are assuming the LCL and UCL figures are sufficiently accurate. If (as seems likely) they have been rounded off to the nearest whole number then the mean and standard deviation will be close but not exactly correct. http://en.wikipedia.org/wiki/Accuracy_and_precision

Also I'm a bit worried that I haven't taken the sample size into account - test questions usually mean for you to use everything that's provided: so it might be a red herring or it might not! I know that's important in calculating std dev the hard way (from the original data) but there's no indication here that you have the original data...
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