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 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 normal distribution is the best choice to model the diameter of the O-rings. The given information that the average diameter is 4.2 cm and approximately 95% of the O-rings have diameters between 3.2 cm and 5.2 cm are characteristics of a normal distribution. Additionally, the fact that almost all of the O-rings have diameters between 2.7 cm and 5.7 cm supports the use of a normal distribution, as this range falls within three standard deviations of the mean for a normal distribution. The uniform distribution would not be appropriate since the probability of a diameter falling within the given range would not be the same for all values. The binomial distribution is not appropriate since it models a discrete probability distribution rather than a continuous distribution. The exponential distribution is not appropriate since it models the time required for an event to occur rather than the distribution of O-ring diameters. The normal distribution is the best choice since it is commonly used to model continuous data such as the diameter of O-rings. The average diameter and the percentage of O-rings falling within certain diameter ranges suggest a normal distribution. The uniform distribution does not fit since not all diameters are equally likely. The binomial distribution is unsuitable since it is used to model discrete data with a fixed number of trials, whereas the diameter is continuous data. The exponential distribution is unlikely to fit as it is used to model the time between events occurring, and there is no clear reason for applying it here.

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