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

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.