Ace the HSC Mathematics Standard 2 Exam 2025 – Unleash Your Math Mastery!

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Which of the following is true about the Z-score?

It determines the position of a value within a distribution

The Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution. This allows for the assessment of the position of a value within the context of the overall distribution. A positive Z-score indicates the value is above the mean, while a negative Z-score indicates it is below the mean. Therefore, the ability to determine the position of a value within a distribution is a fundamental characteristic of the Z-score, making this statement true.

In terms of the remaining options, the Z-score is not always a whole number; it can take any real value, including decimals. Additionally, it is directly related to the mean and standard deviation, as the Z-score formula utilizes both to calculate its value. Lastly, while Z-scores can be used to assess probabilities through the standard normal distribution, they do not calculate probabilities directly.

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It is always a whole number

It is unrelated to the mean or standard deviation

It is used to calculate the probability directly

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