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) for pvc pipe in 2008, the authors estimate a failure rate of 0.0081 failures per 100 miles of pipe per day. consider a 100-mile-long segment of such pipe. what is the expected number of failures in 1 year (365 days)? based on thi

Answer :

The expected number of failures in 1 year is 8.9948.

The authors calculate a failure rate for PVC pipe of 0.0081 per 100 miles of pipe per day in 2008. Think of a 100-mile section of this pipe.

(I)

Given;

Mean failures per day = 0.0081

So,

Expected number of failures in 1 year = 0.0081 * 365

                                                               = 8.9948

(II)

Poisson Distribution with λ = 8.9948 is given by:

[tex]P(x) =\frac{e^-^8^.^9^9^4^8 8.9948^0}{x!}[/tex]

             ⇒ for x = 0, 1, 2,. . . .

P(At least 1 failure) = 1- P(X=0);

[tex]P(x) = \frac{e^-^8^.^9^9^4^8 8.9948^0}{0!} = \frac{0.00012*1}{1}[/tex]

        = 0.00012    

So,

P(At least 1 failure) = 1 - 0.00012 = 0.99988

Hence, the expected number of failures in 1 year is 8.9948.

To learn more about Poisson Distribution click here:

brainly.com/question/17280826

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