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.