Elon Musk
IQ: 160 ± 6
🔍 How Did We Calculate This?
Note: We don't have Elon Musk's SAT scores, so we're using the scores of UPenn and physics major students as proxies. Please treat this as a rough estimation.
1️⃣ Calculating the Percentile of an Average Physics Major Student's IQ:
First, we calculate the percentile of an average physics 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 = (133 - 115) / 15 ≈ 1.2.
2️⃣ Finding the IQ of an Average Physics Student at UPenn:
Next, we assume that the IQ of an average physics student at UPenn is at the same percentile (88th) in the distribution of all UPenn students. To find the corresponding IQ, we reverse the Z-score calculation, using the average IQ of UPenn students (142) as the mean. X = μ + Z * σ = 142 + 1.2 * 15 ≈ 160.
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 160 ± (1.96 * 3) ≈ 160 ± 6.
4️⃣ Final Result:
So, we'd estimate that Elon Musk's IQ is around 160, with a 95% confidence interval of 154 to 166.