Question

What is the IQ score that separates the bottom 20% from the top 80% of IQ scores with 100 and standard deviation a = 16?​ (a) 95

(b) 110
(c) 85
(d) 120

Answer 1

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.