The weight of connecting rods used in an automobile engine is to be closely controlled to minimize vibrations. The specification is that each rod must be 974 1.2 grams. The half-width of the specified interval, namely, 1.2 grams, is known as the tolerance. The manufacturing process at a plant produces rods whose weights are normally distributed with a mean of 973.8 grams and a standard deviation of 0.32 grams.
a. What proportion of the rods produced by this process will be acceptable according to the specification?
e. Suppose the process is adjusted so that the offset is zero, and σ remains at 0.32 gram. Now, what proportion of the parts made by the process will fall within specification limits?
f. A process has a Cp of 1.2 and a Cpk of 0.9. What proportion of the parts produced by the process will fall within specification limits?