Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 6 ounces.**a.** The process standard deviation is 0.10, and the process control is set at plus or minus 1.5 standard deviation $ s $. Units with weights less than 5.85 or greater than 6.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?[Input Box]**In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)?**[Input Box]**b.** Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same with weights less than 5.85 or greater than 6.15 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?[Input Box]**In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?**[Input Box]**c.** What is the advantage of reducing process variation, thereby causing a problem to be at a greater number of standard deviations from the mean?[Input Box: It can substantially reduce the number of defects]

Refer Standard normal table/Z-table OR use excel formula "=NORM.S.DIST(-1.5, TRUE)" &…

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 6 ounces. a. The process standard deviation is 0.10, and the process control is set at plus or minus 1.5 standard deviation s. Units with weights less than 5.85 or greater than 6.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)? b. Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same with weights less than 5.85 or greater than 6.15 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 6 ounces. a. The process standard deviation is 0.10, and the process control is set at plus or minus 1.5 standard deviation s. Units with weights less than 5.85 or greater than 6.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)? b. Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same with weights less than 5.85 or greater than 6.15 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

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!

Question

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 6 ounces.

**a.** The process standard deviation is 0.10, and the process control is set at plus or minus 1.5 standard deviation $ s $. Units with weights less than 5.85 or greater than 6.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

[Input Box]

**In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)?**

[Input Box]

**b.** Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same with weights less than 5.85 or greater than 6.15 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?

[Input Box]

**In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?**

[Input Box]

**c.** What is the advantage of reducing process variation, thereby causing a problem to be at a greater number of standard deviations from the mean?

[Input Box: It can substantially reduce the number of defects]

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