On most modern IQ tests, a score of 115 would be: A. about normal. B. about \(15 \%\) higher than the average of one's agemates. C. an indication of genius. D. one standard deviation above the mean.

Short Answer

Expert verified
A. The score is about normal. B. The score is 15% higher than the average. C. The individual is a genius. D. The score is one standard deviation above the mean. Answer: B, D

Step by step solution

01

Calculate how much higher the given score is from the mean

First, let's find out how much higher the score of 115 is compared to the mean score of 100. We can do this by subtracting the mean from the given score: $$115 - 100 = 15$$
02

Determine as a percentage how much higher the score is from the mean

To calculate this percentage, divide the difference we found in Step 1 by the mean and multiply the result by 100: $$ \frac{15}{100} \times 100 = 15 \% $$
03

Compare the difference to the standard deviation

Next, we need to determine how many standard deviations the given score is above the mean. Divide the difference we found in Step 1 by the standard deviation (15): $$ \frac{15}{15} = 1 $$ The given score is one standard deviation above the mean.
04

Select the correct answer

Now we can analyze the provided options: A. The given score is 15% higher than the average, so "about normal" isn't accurate. B. We calculated the score is 15% higher than the average, so this statement is true. C. A score of 115 doesn't represent genius-level intelligence, so this is false. D. Our calculations showed one standard deviation above the mean, so this statement is true. Therefore, the correct answer choices are B and D.

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