Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What percentage of people have an IQ score higher than 66, to the nearest tenth?

Answer 1

We need to find the area under the standard normal curve that is to the right of 66.

Various ways of doing this include the following:

1) Calculator:  normalcdf(66, 10000, 100, 15) = 0.988, or 98.8%

2) z-scores (using a published table of z scores)
                                                                                      66 - 100
     a)  Find the z score corresponding to 66.  It is z = -------------- = -2.27
                                                                                             15

      b) Find the area under the st. normal curve to the left of z=-2.27 (it is                   0.012).  Subtract that area from the total area, 1.000.  The result will                be the answer to this question.