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Which of these z-scores might represent a very difficult item in the normal distribution?a.+2.33b.−.52c.−2.06d.+.20

Question

Which of these z-scores might represent a very difficult item in the normal distribution?a.+2.33b.−.52c.−2.06d.+.20

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Solution

In a normal distribution, a z-score represents how many standard deviations an element is from the mean. A positive z-score indicates the data point is higher than the mean, while a negative z-score indicates it is lower.

In the context of a test item's difficulty, a very difficult item would be one that few people answer correctly. This would be represented by a low score, which in a normal distribution would be a negative z-score.

Therefore, the z-score that might represent a very difficult item in the normal distribution would be -2.06 (option c), as it is the most negative and thus represents a score significantly below the mean.

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