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The percentile of a value chosen from a set of observations is the percentage of observations that fall below the chosen value.
In the IQ test, the mean is 100 and the standard deviation 15.
To determine the percentile that a score 114 is in, find the z-score of 114. This is equal to (114 - 100)/15 = 0.9333. Using a normal table, the value for 0.933 is 0.8238. 114 is in the 82.38th percentile. For 140, the z-score is 2.67. The value for 2.67 from a normal distribution table is 0.9962. 140 lies in the 99.62th percentile.
From the normal distribution table, the z-score corresponding to 99% is 2.41. The score corresponding to this is 136.15
The percentile a person with a score of 114 is in is 82.38. A score of 140 lies in the 99.62th percentile and the minimum score that lies in the 99th percentile is 136.15
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