# High IQ Exercise 26 proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.

Question
Modeling
High IQ Exercise 26 proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.

2021-02-26
Step 1 Any IQ more than 132 might be considered as unusually high. The given information is that the modeling IQ scores follow normal distribution with mean $$\mu=16\ \text{and standard deviation} \sigma = 16.$$ Let the random variable Y represents the IQ scores. The IQ more than three standard deviations below the mean is expected to see very rarely. The corresponding IQ can be obtained as follows: $$\mu\ +\ 3 \sigma = 100\ +\ 3(16) = 100\ +\ 48 = 148$$ Thus, there is very rare chance to find someone with an IQ over 148. Step 2 Generally any IQ scores more than two standard deviations above the mean is considered as unusually high. The corresponding IQ score can be obtained as follows: $$\mu\ +\ 2\ \sigma = 100\ +\ 2(16) = 100\ +\ 32 = 132$$ Thus, there are more than 132 are considered as unusually high IQ scores.

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