The thickness of a part is to have an upper specification of

The thickness of a part is to have an upper specification of 0.925 and a lower specification of 0.870 mm. The average of the process is currently 0.917 with a standard deviation of 0.005. Determine the percentage of product that meet the specification.

Solution

f(x) = f(0.9)
f(0.9) = 1 - f(z)
f(x > 0.9) = f(z)


z = x - /
z = 0.9 - 0.917 / 0.005
z = -3.4 (left curve)

1 - f(z) = 0.0033693
f(z) = f(x>0.9) = 0.9966307
f(x>0.9) = 99.66307 %