Final answer:
The IQ score that separates the bottom 20% from the top 80% with a mean of 100 and standard deviation of 16 is approximately 113.47.
Step-by-step explanation:
To find the IQ score that separates the bottom 20% from the top 80% of IQ scores, we need to find the z-score associated with the 80th percentile. The z-score can be calculated using the formula:
z = (x - μ) / σ
where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation. Rearranging the formula to solve for x:
x = z * σ + μ
Using the given mean IQ score of 100 and standard deviation of 16, we find that the z-score associated with the 80th percentile is approximately 0.8416. Plugging the values into the formula:
x = 0.8416 * 16 + 100 ≈ 113.47
Therefore, the IQ score that separates the bottom 20% from the top 80% is approximately 113.47.