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Yet another time, you find yourself the quality control manager for the Acme Widget Company. You are concerned about the number of defective widgets being produced by one of your factories. (a) You have determined that the number of defective widgets pro- duced per day by your factory has a mean of 10. You claim that the probability that your factory produces 15 or more de- fective widgets per day is less than or equal to 0.5. Is this claim justified? Explain your answer mathematically. (b) You have have determined that the number of defective widgets produced per day by your factory is approximately a normal distribution with mean 10 and variance 5. You claim that the probability that your factory produces 15 or more defective wid- gets per day is less than or equal to 0.02. Is this claim justified? Explain your answer mathematically.

Yet another time, you find yourself the quality control manager for the Acme Widget Company. You are concerned about the number of defective widgets being produced by one of your factories. (a) You have determined that the number of defective widgets pro- duced per day by your factory has a mean of 10. You claim that the probability that your factory produces 15 or more de- fective widgets per day is less than or equal to 0.5. Is this claim justified? Explain your answer mathematically. (b) You have have determined that the number of defective widgets produced per day by your factory is approximately a normal distribution with mean 10 and variance 5. You claim that the probability that your factory produces 15 or more defective wid- gets per day is less than or equal to 0.02. Is this claim justified? Explain your answer mathematically.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Need help with this problem a and b

Yet another time, you find yourself the quality control manager for the Acme Widget Company. You are concerned about the number of defective widgets being produced by one of your factories. (a) You have determined that the number of defective widgets pro- duced per day by your factory has a mean of 10. You claim that the probability that your factory produces 15 or more de- fective widgets per day is less than or equal to 0.5. Is this claim justified? Explain your answer mathematically. (b) You have have determined that the number of defective widgets produced per day by your factory is approximately a normal distribution with mean 10 and variance 5. You claim that the probability that your factory produces 15 or more defective wid- gets per day is less than or equal to 0.02. Is this claim justified? Explain your answer mathematically.
Transcribed Image Text:Yet another time, you find yourself the quality control manager for the Acme Widget Company. You are concerned about the number of defective widgets being produced by one of your factories. (a) You have determined that the number of defective widgets pro- duced per day by your factory has a mean of 10. You claim that the probability that your factory produces 15 or more de- fective widgets per day is less than or equal to 0.5. Is this claim justified? Explain your answer mathematically. (b) You have have determined that the number of defective widgets produced per day by your factory is approximately a normal distribution with mean 10 and variance 5. You claim that the probability that your factory produces 15 or more defective wid- gets per day is less than or equal to 0.02. Is this claim justified? Explain your answer mathematically.
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Step 1: Introduction to the given problem

We are given two different scenarios and asked whether the claims in each scenario are justified or not.

a) You have determined that the number of defective widgets produced per day by your factory has a mean of 10. You claim that the probability that your factory produces 15 or more defective widgets per day is less than or equal to 0.5.

b) You have determined that the number of defective widgets produced per day by your factory is approximately a normal distribution with a mean of 10 and a variance of 5. You claim that the probability that your factory produces 15 or more defective widgets per day is less than or equal to 0.02.

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