Question

3. The outside diameter of a part used in a gear assembly is known to be normally distributed with a mean of 39 mm and a standard deviation of 2.5 mm. The specifications on the diameter are (36,45), which means that part diameters between 36 mm and 45 mm are considered acceptable.

1. What is the proportion nonconforming?
2. What is Z bench?
3. If the mean of the process was centered between the specs, what would the proportion non-conforming be?

Answer 1

Proportion conforming = P(36 X 45)

= P(X 45) - P(X 36)

= P[Z (45 - 39)/2.5] - P[Z (36 - 39)/2.5]

= P[Z 2.4] - P[Z -1.2]

= 0.9918 - 0.1151

= 0.8767

Proportion nonconforming = 1 - Proportion conforming = 1 - 0.8767 = 0.1233

Z bench = Z value for x( = 0.1233) = -1.1586

If the mean of the process was centered between the specs, then the outside diameter of a part used in a gear assembly is known to be normally distributed with a mean of (45+36)/2 = 40.5 mm and a standard deviation of 2.5 mm

Proportion conforming = P(36 X 45)

= P(X 45) - P(X 36)

= P[Z (45 - 40.5)/2.5] - P[Z ​​​​​​​ (36 - 40.5)/2.5]

= P[Z 1.8] - P[Z -1.8]

= 0.9641 - 0.0359

= 0.9282

Proportion nonconforming = 1 - Proportion conforming = 1 - 0.9282 = 0.0718