QQuestionStatistics
QuestionStatistics
For a person with an IQ of 145, his or her score would be _____ standard deviations above the normative mean.
Possible answers:
A. 1
B. 2
C. 3
D. 4
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand IQ Distribution
- IQ scores are designed to follow a normal distribution - The mean (average) IQ is set at 100 - The standard deviation for IQ is typically 15 points
Step 3:: Calculate the Deviation
- Calculation: $$\frac{145 - 100}{15} = \frac{45}{15} = 3
- A person with an IQ of 145 is above the mean of 100 - To find how many standard deviations this is, we subtract the mean and divide by the standard deviation
Step 4:: Interpret the Result
- The calculation shows that 145 is 3 standard deviations above the mean - This means the person's IQ is extremely high, being in the top 0.1% of the population
Final Answer
Key Insights: - Standard deviation helps measure how far a value is from the mean - In a normal distribution, about 68% of values are within 1 standard deviation, 95% within 2, and 99.7% within 3
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