Defective Tube Estimation Using Central Limit Theorem

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SUMMARY

The discussion centers on estimating the number of defective tubes using the Central Limit Theorem. Given a mean cross-sectional area (u) of 12.5 and a standard deviation (SD) of 0.2, the user correctly normalized the variables to Z values, calculating the probability of defects for areas less than 12 and greater than 13. The final estimation indicates approximately 12 defective tubes in a shipment of 1000. The user confirmed that no correction factor is necessary for this calculation.

PREREQUISITES
  • Understanding of Central Limit Theorem
  • Knowledge of Z-score normalization
  • Familiarity with probability distributions
  • Basic statistics concepts, including mean and standard deviation
NEXT STEPS
  • Study the application of the Central Limit Theorem in quality control
  • Learn about binomial approximation and its correction factors
  • Explore advanced statistical methods for defect estimation
  • Investigate the implications of standard deviation in manufacturing processes
USEFUL FOR

Statisticians, quality control analysts, and students in statistics or engineering fields who are involved in defect estimation and quality assurance processes.

rhyno89
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Homework Statement



The cross sectional area of a tube is u = 12.5 and SD = .2. When the area is less than 12 or greater than 13 it won't work. They are shipped in boxes of 1000, determine how many per box will be defective

Homework Equations





The Attempt at a Solution



So I think I have the solution but am a little confused with the process. To start I normalized the variables into Z values. So I did (12-12.5)/.2 and (13-12.5)/.2. When it was all said and done I found it to equal .0124 x 1000 = aprx 12 defects.

My question is do I have to add any correction factor while normalizing like for the binomial approximation and do I have to change the mean. I know that some types of these problems require me to start by multiplying the mean by the number and doing a similar change to the standard deviation. I don't really need much help with the computation, just getting a little confused with all the different cases.

Thanks a lot
 
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Nope - you followed the correct steps: use the information to find the chance an item will be defective, then estimate the number in your shipment that will be defective.
 

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