9. Suppose that we have a normally distributed process such that 11-60 and ?-4 w

Question

9. Suppose that we have a normally distributed process such that 11-60 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

a)
99.7% of our future product fall within 3sigma
mu +/- 3sigma = 60+/-3*0.4 = 958.8,61.2)

b)
59.6 and 60.4 will fall between 68.269%
mu +/- 1 sigma = 60 +/- 0.4= (59.6 , 60.4)

c)
mu - lower spec limit = 60 -0.5 = 59.5 to be in spec most of the time
So, std.deviation = 0.5/3 = 0.167

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