a school psychologist has a particular IQ test for whick of the population mean is 100 and the standard deviation 15. A group of 45 tenth graders in an advanced class based on school performance was given the IQ test, and that were found to have an average IQ of 123. Determine whether this is significantly higher than the average for the population.

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What you have to do is look at the probability distribution of a normal curve and the probability densities at different standard deviation lengths away from the mean. 1 standard deviation above the mean is in the better than 84.1% of the population which would be a score of 115. 2 standard deviations above the mean would be a score of 130 and would be better than 97.7% of the population. The score of 123 is between 1 and 2 standard deviations and thus the average IQ of this class would be around the low to mid 90's% better than the average population which is sign that the IQ of the class is significantly higher than the average for the population.

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