Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations. (a)The process standard deviation is 0.36, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.64 or greater than 10.36 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number. Probability of a defect: Number of defects: (b)Through process design improvements, the process standard deviation can be reduced to 0.12. Assume that the process control remains the same, with weights less than 9.64 or greater than 10.36 ounces being classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number. Probability of a defect: Number of defects: (c)What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean? Reducing the process standard deviation causes a - Select your answer -substantial increasemoderate increasenegligible changemoderate decreasesubstantial decreaseItem 5 in the number of defects.

a). Given, μ=10σ=0.36n=1000Let X be the weight of the itemThus, X~Nμ=10,σ= Now the product is…

Answered: Suppose that Motorola uses the normal…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

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Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.

(a)

The process standard deviation is 0.36, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.64 or greater than 10.36 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.

Probability of a defect:
Number of defects:

(b)

Through process design improvements, the process standard deviation can be reduced to 0.12. Assume that the process control remains the same, with weights less than 9.64 or greater than 10.36 ounces being classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.

Probability of a defect:
Number of defects:

(c)

What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

Reducing the process standard deviation causes a - Select your answer -substantial increasemoderate increasenegligible changemoderate decreasesubstantial decreaseItem 5 in the number of defects.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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