A quality control manager at a plant that produces o-rings is concerned about whether the diameter of the o-rings that are produced is conformable to the specification.She has calculated that the average diameter of the o-rings is 4.2 centimeters.She also knows that approximately 95% of the o-rings have diameters that fall between 3.2 and 5.2 centimeters and almost all of the o-rings have diameters between 2.7 and 5.7 centimeters.When modeling the diameters of the o-rings,which distribution should the scientists use?
A)Uniform distribution
B)Binomial distribution
C)Normal distribution
D)Exponential distribution

Question

Quizplus · Accepted Answer

The fact that the average diameter is given, and about 95% of the o-rings fall within a specific range, suggests a normal distribution. Additionally, the fact that almost all of the o-rings fall in a broader range (2.7 to 5.7 centimeters) further supports the normal distribution as it implies symmetry around the mean. A uniform distribution would not be appropriate since there is not an equal likelihood of any diameter within a specified range. A binomial distribution would be appropriate if we were interested in the number of o-rings meeting a specific diameter requirement (i.e. pass/fail), but we are interested in the distribution of diameters themselves. An exponential distribution would not be appropriate since it is used for modeling the time between events occurring, which is not applicable in this case.

A Quality Control Manager at a Plant That Produces O-Rings