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

Question
Modeling
asked 2021-02-25
High IQ Exercise 26 proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.

Answers (1)

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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