Since the mean is 100 and the SD is 20. Note for 140 IQ score, you are 2
standard deviations above the mean.
That means you scored higher than 97.5% of the people who took the IQ
That is 97.5% of the area under the normal curve. Remember the Empirical
That is, 68% of the data is within one SD, 95% of the data is within 2 SD,
and 99.7% of the data is within 3 SD. Therefore, 50+34+13.5=97.5.
Suppose someone had a 180 IQ. That means they would be 4 SD above
the mean. That would correspond to .999968328283
That means they would score higher than 99.9968% of the others.
If 1,000,000 took the test, that means only about 32 out of 1 million
would score as high or higher.
For your 140 score, if 1 million took the test, about 25,000 out of the
million would score as higher or higher than 140.
See now a wee bit better?.