Motorola used the normal distribution to determine the probability of defects expected in a production process. Assume a production process produces items with a mean weight of 11 ounces. a. The process standard deviation is 0.14, and the process control is set at plus or minus 2.4 standard deviations. Units with weights less than 10.664 or greater than 11.336 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? b. Through process design improvements, the process standard deviation can be reduced to 0.12. Assume the process control remains the same, with weights less than 10.664 or greater than 11.336 ounces being classified as defects. What is the probability of a defect (to 4 decimals)?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Motorola used the
a. The process standard deviation is 0.14, and the process control is set at plus or minus 2.4 standard deviations. Units with weights less than 10.664 or greater than 11.336 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?
b. Through process design improvements, the process standard deviation can be reduced to 0.12. Assume the process control remains the same, with weights less than 10.664 or greater than 11.336 ounces being classified as defects. What is the probability of a defect (to 4 decimals)?
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