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How to tell which of two z-scores is more extreme?

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Final answer:

To determine which z-score is more extreme, compare the absolute values of the z-scores. The one with the larger absolute value is more extreme, as it represents more standard deviations away from the mean. Z-tables can also be used to gauge the extremity by showing lesser area to the right of more extreme z-scores.

Step-by-step explanation:

To determine which of two z-scores is more extreme, you should compare their absolute values, regardless of whether they are positive or negative. The z-score represents how many standard deviations a value is from the mean. By looking at the absolute value of the z-score, we can tell how far a value is from the mean, which is indicative of its extremity in the context of a normal distribution.

For instance, a z-score of +3 is more extreme than a z-score of +2 since its absolute value is greater, indicating that it is farther from the mean. The empirical rule, also known as the 68-95-99.7 rule, can be a helpful guideline. It states that approximately 68% of values fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This tells us that a z-score of +3 (or -3) is more extreme than a z-score of +2 (or -2), as it lies further out in the tails of the normal distribution curve.

Z-tables can also be utilized to determine the extremity of z-scores. These tables provide the area under the normal curve to the left of a given z-score. Greater absolute z-score values correspond to smaller areas to the right of the z-score (or larger areas to the left), indicating a more extreme value.

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