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Approximately what percentile rank is associated with a z-score of +1.00?

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Final answer:

A z-score of +1.00 is typically associated with the 84th percentile in a normal distribution. The empirical rule helps us estimate that roughly 68% of values lie between z-scores of -1 and +1, indicating that 84% lie below the z-score of +1.

Step-by-step explanation:

A z-score of +1.00 typically corresponds to a percentile rank of approximately the 84th percentile.

This can be understood by recognizing that a z-score measures how many standard deviations an element is from the mean of a distribution.

The empirical rule, also known as the 68-95-99.7 rule, suggests that approximately 68% of values in a normal distribution lie between z-scores of -1 and +1.

Since the distribution is symmetric, half of this 68% will lie below the mean and half above. Consequently, the total area under the normal curve to the left of a z-score of +1 is roughly 50% (percent of values below the mean) plus 34% (half of 68%), which combined gives you approximately 84%.

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