Courtney Cox
IQ: 118 ± 18
🔍 How Did We Calculate This?
Note: Courtney Cox's SAT score is 1150, which we used as the foundation for our IQ estimate.
1️⃣ SAT to IQ Conversion:
Using the formula IQ = 39.545 + 0.068 × SAT score, we estimated her IQ to be around 118.
2️⃣ Calculating the Standard Error:
The correlation between SAT scores and IQ is 0.8. To account for the unexplained variance (20%), we calculate the standard error (SE) using the formula SE = SD × √(1 - r²), where SD is the standard deviation of IQ scores (assumed to be 15) and r is the correlation coefficient (0.8). This results in a SE of approximately 9.
3️⃣ Determining the Margin of Error:
For a 95% confidence interval, the z-score is 1.96. The margin of error (MOE) is calculated using MOE = z * SE. Thus, MOE = 1.96 × 9 ≈ 18.
4️⃣ Final Result:
Adding and subtracting the MOE from the estimated IQ gives us the confidence interval. Therefore, Courtney Cox's IQ is estimated to be 118 with a 95% confidence interval of approximately 118 ± 18, which translates to a range from about 100 to 136.