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Fofino [41]
3 years ago
7

The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard d

eviation 7.8 mm [suggested in the article "Reliability Evaluation of Corroding Pipelines Considering Multiple Failure Modes and Time-Dependent Internal Pressure" (J. of Infrastructure Systems, 2011: 216–224)].
What values separate the largest 80% from the smallest 20% of the defect length distribution.
Mathematics
1 answer:
skelet666 [1.2K]3 years ago
8 0

Answer:

z=-0.842

And if we solve for a we got

a=30 -0.842*7.8=23.432

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

Step-by-step explanation:

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(30,7.8)  

Where \mu=30 and \sigma=7.8

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.80   (a)

P(X   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.842

And if we solve for a we got

a=30 -0.842*7.8=23.432

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

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