Defective Tube Estimation Using Central Limit Theorem

In summary, the cross sectional area of a tube is u = 12.5 and SD = .2. If the area is less than 12 or greater than 13, it won't work. The tubes are shipped in boxes of 1000 and there will be approximately 12 defective tubes per box. The correct steps to find this estimation are to normalize the variables into Z values and use that information to determine the chance of an item being defective.
  • #1
rhyno89
21
0

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 alot
 
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  • #2
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.
 

Related to Defective Tube Estimation Using Central Limit Theorem

1. What is the central limit theorem?

The central limit theorem is a statistical concept that states that the sample mean of a large enough sample will tend to follow a normal distribution, regardless of the distribution of the original population.

2. Why is the central limit theorem important?

The central limit theorem is important because it allows us to make inferences and predictions about a population based on a sample, without knowing the underlying distribution of the population. It is also the basis for many statistical methods and models.

3. How is the central limit theorem used in practice?

The central limit theorem is used in practice to estimate population parameters, test hypotheses, and make predictions. For example, if a company wants to know the average age of their customers, they can take a sample and use the central limit theorem to estimate the population mean age.

4. What are the assumptions of the central limit theorem?

The central limit theorem assumes that the sample is random, the sample size is large enough, and the sample observations are independent of each other. It also assumes that the population has a finite variance.

5. Can the central limit theorem be applied to any sample size?

No, the central limit theorem holds true for large enough sample sizes. As a general rule, a sample size of 30 or more is considered large enough for the central limit theorem to be applicable. However, the larger the sample size, the more accurate the results will be.

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