Nondestructive evaluation: Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means such as X-ray computed tomography, ultrasonics, and acoustic emission. Recently, NDE was used to detect defects in steel castings. (JOM, May 2005.) Assume that the probability that NDE detects a "hit" (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a "hit" when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experience has shown that a defect occurs once in every 100 steel castings. If NDE detects a "hit" for a particular steel casting, what is the probability that an actual defect exists?

Nondestructive evaluation: Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means such as X-ray computed tomography, ultrasonics, and acoustic emission. Recently, NDE was used to detect defects in steel castings. (JOM, May 2005.) Assume that the probability that NDE detects a "hit" (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a "hit" when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experience has shown that a defect occurs once in every 100 steel castings. If NDE detects a "hit" for a particular steel casting, what is the probability that an actual defect exists?

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Nondestructive evaluation: Nondestructive evaluation (NDE) describes methods
that quantitatively characterize materials, tissues, and structures by noninvasive
means such as X-ray computed tomography, ultrasonics, and acoustic emission.
Recently, NDE was used to detect defects in steel castings. (JOM, May 2005.)
Assume that the probability that NDE detects a "hit" (i.e., predicts a defect in a steel
casting) when, in fact, a defect exists is .97. (This is often called the probability of
detection.) Also assume that the probability that NDE detects a "hit" when, in fact,
no defect exists is .005. (This is called the probability of a false call.) Past experience
has shown that a defect occurs once in every 100 steel castings. If NDE detects a
"hit" for a particular steel casting, what is the probability that an actual defect
exists?

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