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

Efan Halliday 2021-02-25 Answered
High IQ Exercise 26 proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.
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brawnyN
Answered 2021-02-26 Author has 91 answers

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 μ=16 and standard deviationσ=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: μ + 3σ=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: μ + 2 σ=100 + 2(16)=100 + 32=132 Thus, there are more than 132 are considered as unusually high IQ scores.

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