Short Answer 
Oprah Winfrey has a Z-score of 2.73, which indicates her IQ is approximately 140.95, significantly above the average IQ of 100. This Z-score also places her in the 99.68 percentile, meaning she performs better than about 99.68% of the population, showcasing her exceptional cognitive abilities.
Step 1: Understand the Z-score
The Z-score is a statistical measure that indicates how far an individual score is from the average score, expressed in terms of standard deviations. In Oprah Winfrey’s case, her Z-score is 2.73, which means her IQ score is 2.73 standard deviations above the mean. Here’s how it works:
- The average IQ is set at 100.
- Each standard deviation in IQ is 15 points.
- Thus, an IQ score can be calculated using the formula: Mean + (Z-score ‚àöo Standard Deviation).
Step 2: Calculate Oprah’s IQ
Using her Z-score, we can convert it to an approximate IQ score. Since her Z-score is 2.73, we can plug it into the formula mentioned above. By doing so:
- Oprah’s approximate IQ is calculated as: 100 + (2.73 ‚àöo 15).
- This results in a score of approximately 140.95, indicating a high IQ.
- This score shows that she is quite above the average IQ level.
Step 3: Determine the Percentile Rank
The conversion of a Z-score to a percentile rank helps to understand how an individual compares to the population. For Oprah’s Z-score of 2.73, we refer to the standard Z-score tables:
- The Z-score table indicates a percentile rank of 99.68% for Z=2.73.
- This means Oprah’s performance is better than approximately 99.68% of the tested population.
- Such a high rank is indeed exceptional and highlights her advanced cognitive abilities.