IQ scores are known to be normally distributed. The mean IQ score is 100 and the standard deviation is 15. The top 25% of the population (ranked by IQ score) have IQ’s above what value?
Answers
Answer:
75%
Explanation:
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106
Explanation:
The average of 25 people is a summary statistic, and as a result will have a smaller standard deviation than an individual’s IQ standard deviation. The standard deviation will be smaller by a factor equal to the square root of the sample size. So take the individual standard deviation and divide it by the square root of 25. 15/√25 = 3
Next step is to get a z-score by calculating [y - y(avg)]/std dev
[106 - 100]/3 = 2, your z-score is +2.
Your next step is to find the percent for a +1.875 z-score. According to my z-table this is 97.72%, but z-tables are designed to show when you are under the stated value, this question wants you to be over the stated value, so 100% - 97.72% = 2.28%.
There is approximately a 2.28% probability your 25 person average will exceed 106 points.