Question

based on what you know about the empirical rule and z-scores, and assuming a normal distribution, what is the approximate percentile rank of a value that is associated with a z-score of 0?

Answer 1

According to the empirical rule, z-scores, and supposing a normal distribution, a number with a z-score of 0 has an estimated percentile rank of 50.

Define the term empirical rule in normal distribution?

A statistical principle known as the empirical rule, also known as the three rule or 68-95-99.7 rule, holds that with a normal distribution, mostly all observed data will lie around three standard deviations (signified by σ ) of the mean or average (signified by µ ).

• In accordance with the Empirical Rule, 99.7% of data that are found to have a normal distribution fall around 3 standard deviations from the mean.
• According to this formula, 68% of the data are within one standard deviation of the mean, 95% are within two deviations, and 99.7% are within three standard deviations.

Thus, as per the empirical rule, z-scores, and supposing a normal distribution, a number with a z-score of 0 has an estimated percentile rank of 50.

To know more about the empirical rule, here

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