Short Answer 
The Z-score is a statistic indicating how far a score is from the average, with Oprah Winfrey having a Z-score of 2.73, translating to an estimated IQ of about 140.95. Additionally, her Z-score corresponds to a percentile rank of approximately 99.68%, meaning she outranks 99.68% of the population in terms of IQ.
Step 1: Understanding Z-scores
The Z-score is a statistical measure that tells us how far away an individual’s score is from the average. It represents the number of standard deviations a score is from the mean. For instance, Oprah Winfrey has a Z-score of 2.73, indicating her IQ is significantly above the average score.
Step 2: Calculating Oprah’s IQ
To find Oprah’s actual IQ score from her Z-score, we use the formula: IQ = Mean + (Z-score √ó Standard Deviation). In this case, the mean IQ score is set at 100, and the standard deviation for IQ is 15. Thus, Oprah’s IQ calculation would look like this:
- IQ = 100 + (2.73 √ó 15)
- This results in an IQ score of approximately 140.95.
Step 3: Determining Percentile Rank
The next step is converting the Z-score into a percentile rank. This informs us what percentage of the population has a lower score than Oprah. Using a standard Z-table, the Z-score of 2.73 gives a percentile rank of about 99.68%. This means Oprah’s IQ is higher than approximately 99.68% of the tested population, illustrating her exceptional intelligence.