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Which of the following is not true? Choose the correct answer below. A. A z-score is an area under the normal curve. B. If values are converted to standard \( z \)-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution. C. A z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. D. The area in any normal distribution bounded by some score \( x \) is the same as the area bounded by the equivalent \( z \)-score in the standard normal distribution.

Ask by Osborne Hills. in the United States
Feb 28,2025

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Tutor-Verified Answer

Answer

A z-score is not an area under the normal curve.

Solution

The correct answer is A. Explanation: A z-score is a standardization of a data value, not an area under the curve. It represents how many standard deviations a given value is from the mean. The other three options accurately describe aspects of converting and understanding normal distributions when using z-scores.

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Bonus Knowledge

A z-score is indeed a statistical measure that indicates how many standard deviations a data point is from the mean, but it is not an area under the normal curve—it’s a single value representing a position on that curve. So it’s safe to say that option A falls short of the mark! If you're diving deeper into z-scores, consider this fun fact: They play a vital role in fields like psychology and education, where they're used to compare test scores from different distributions. It helps normalize data to assess performances fairly—turning chaotic numbers into a beautiful symphony of normality!

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