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## Bill Gates

### IQ: 157 ± 6

#### 🔍 How Did We Calculate This?

**Note:** While Bill Gates' SAT score is known to be 1590, this is very close to the upper limit of the scale (1600), and the error would be unusually large at this stage to use it for estimating his IQ. Therefore, it's more precise to use his college major as a proxy. Although Gates' declared major was pre-law, he passed Harvard's most advanced math class. It's therefore fair to group him with Mathematics majors for this estimation.

##### 1️⃣ Calculating the Percentile of an Average Mathematics Major Student's IQ:

First, we calculate the percentile of an average Mathematics major student's IQ in a population of all students. Assuming that the *IQ scores are normally distributed*, we use the Z-score formula to find the percentile. Z = (X - μ) / σ = (130 - 115) / 15 ≈ 1.0.

##### 2️⃣ Finding the IQ of an Average Mathematics Student at Harvard:

Next, we assume that the IQ of an average Mathematics student at Harvard is at the same percentile (84th) in the distribution of all Harvard students. To find the corresponding IQ, we reverse the Z-score calculation, using the average IQ of Harvard students (142) as the mean. X = μ + Z * σ = 142 + 1.0 * 15 = 157.

##### 3️⃣ Adjusting for SAT Scores and IQ Correlation:

Finally, we add a range to account for the fact that SAT scores and IQ have a correlation of 0.8, not 1. This means that *20% of the variation in IQ isn't explained by SAT scores*. Assuming that this unexplained variation is normally distributed, we estimate a 95% confidence interval around our estimate. For a normal distribution, 95% of values lie within 1.96 standard deviations of the mean. Therefore, the 95% confidence interval is 157 ± (1.96 * 3) ≈ 157 ± 6.

##### 4️⃣ Final Result:

So, we'd estimate that Bill Gates' IQ is around 157, with a 95% confidence interval of 151 to 163.

**Note:** All these calculations are based on a number of assumptions and should be taken with a grain of salt. They provide a rough estimate, but the true value could be higher or lower.