Blank 1: Is an IQ score of 125 in the top 5% of the US population (i.e. is a score of 125 above the 95th percentile?) Enter ‘yes’ or ‘no’. Blank 2: What is the exact percentile of a raw score of 125? Include 1 place after the decimal, no % sign is needed (xx.x) Blank # 1 yes Blank # 2 Question 30 (3 points) What percent of the population would you expect to have an IQ lower than 80? Include one space after the decimal, no % sign is needed (x.x)
The Correct Answer and Explanation is:
Blank 1: Yes
An IQ score of 125 is generally considered above average and typically falls above the 95th percentile of the general population in the U.S. This is because the average IQ score is set at 100, and the standard deviation (SD) for most IQ tests is 15.
- A score of 125 is one standard deviation above the mean (100 + 15 = 115), and since 125 is closer to 130 (another standard deviation), it puts you in a higher percentile.
- Based on the normal distribution of IQ scores, 125 is above the 95th percentile, which includes the top 5% of the population. Therefore, an IQ score of 125 is indeed in the top 5%.
Blank 2: 94.1
The exact percentile for a raw score of 125 can be calculated using the Z-score formula for a normal distribution:Z=X−μσZ = \frac{X – \mu}{\sigma}Z=σX−μ
Where:
- X=125X = 125X=125 (the IQ score),
- μ=100\mu = 100μ=100 (the mean IQ),
- σ=15\sigma = 15σ=15 (the standard deviation).
First, calculate the Z-score for a score of 125:Z=125−10015=2515=1.67Z = \frac{125 – 100}{15} = \frac{25}{15} = 1.67Z=15125−100=1525=1.67
A Z-score of 1.67 corresponds to a cumulative percentile of approximately 94.1% in the standard normal distribution. This means that an IQ score of 125 is at the 94.1st percentile, or just above 94% of the population.
Percent of Population with IQ Lower than 80:
To calculate the percentile for an IQ of 80, use the same process as above:Z=80−10015=−2015=−1.33Z = \frac{80 – 100}{15} = \frac{-20}{15} = -1.33Z=1580−100=15−20=−1.33
A Z-score of -1.33 corresponds to about 9.1% of the population. Therefore, you would expect about 9.1% of the population to have an IQ lower than 80.
Answer: 9.1
