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QuestionStatistics
a. If your IQ is 130, the average population IQ is 100, and the standard deviation is 15, what is your z-score?
b. How many standard deviations are above the mean?
c. What does that suggest about your IQ compared to the population?
d. If the average IQ of the population is 100 and the standard deviation is 15, what is the 95 percent confidence interval?
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Calculate the Z-Score
z = \frac{130 - 100}{15} = \frac{30}{15} = 2
Where:
Step 3:: Interpret the Z-Score
The z-score of 2 means you are 2 standard deviations above the mean.
Step 4:: Population Comparison
A z-score of 2 indicates that your IQ is significantly higher than the average population: - Approximately 95.4% of the population has an IQ between - 2 and + 2 standard deviations - You are in the top 2.5% of the population in terms of IQ
Step 5:: 95% Confidence Interval Calculation
Upper bound: $$129.4
The 95% confidence interval is calculated as:
Final Answer
a. Z-score: 2 b. Standard deviations above mean: 2 c. Your IQ is in the top 2.5% of the population d. 95% Confidence Interval: [70.6, 129.4]
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