9, suppose that we have a normally distributed process such that ?-60 and ?-.4 .

Question

9, suppose that we have a normally distributed process such that ?-60 and ?-.4 . within 1 within 2 ? within 3 ? within 4 ? 68269 95450 99730 99993666 A Lot of the Population Most of the Population All but about 6 out of 100,000 a) Where will about 99.7% of our future product fall? b) Written as a percentage, how much of our future product will fall between 59.6 and 60.4? c) Suppose that a customer wants us to manufacture a product that has a lower spec limit of 59.5 and an upper spec limit of 60.5. What do we have to lower the process standard deviation to in order to be in spec most of the time?

Explanation / Answer

Answer to the question :

Mu = 60,

Sigma = .4

So, a. 99.7% of our future products falls within 3 deviations, i.e. 60-3*.4 to 60+3*.4

= 58.8 and 61.2

b. 59.6 and 60.4 are 1 deviation from the mean. Hence, 68.27% of future products fall between 59.6 and 60.4

c. So, if you want to do this withiin the specific limits of 59.5 and 60.5 i.e. within .5 deviation you would

have to capture most ( 99.7%) of data within this .5. So, lower it to .5/3 = .167

New stdev such that the almost all product is within spec limit is .167

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