Newspaper Reports IQ to be 180 | Is it True?

I was reading TheAge. Google is bringing out Google Wave. As part of the story they interview an Australian engineer on the project:

"Nigel, who has an IQ of 180, is also a maths whiz.." - The Age

This got me thinking. What does it mean to have a 180 IQ. IQ is a norm score. IQ typically has a mean of 100 and a standard deviation of 15. Thus, I asked the following questions:

• What's the probability of having an IQ of 180 or higher?
• One in how many people would have an IQ 180 or higher?
• What's is the probability that someone who a newspaper reports as having a 180 IQ or higher, actually has an IQ of 180 or higher?

I decided to do some armchair stats in R:

iqValues = seq(100, 180, 5);
pThisIqOrHigher = 1 - pnorm(iqValues, mean = 100, sd = 15);
oneInThisMany = 1 / pThisIqOrHigher;
pThisIqOrHigherFormatted = formatC(pThisIqOrHigher, 
  digits = 8, format = "f");
oneInThisManyFormatted = formatC(oneInThisMany, 
  digits = 0, width = 10, format = "f");
cbind(IQ=iqValues, p=pThisIqOrHigherFormatted, 
OneIn=oneInThisManyFormatted)  
#       IQ    p            OneIn       
#  [1,] "100" "0.50000000" "         2"
#  [2,] "105" "0.36944134" "         3"
#  [3,] "110" "0.25249254" "         4"
#  [4,] "115" "0.15865525" "         6"
#  [5,] "120" "0.09121122" "        11"
#  [6,] "125" "0.04779035" "        21"
#  [7,] "130" "0.02275013" "        44"
#  [8,] "135" "0.00981533" "       102"
#  [9,] "140" "0.00383038" "       261"
# [10,] "145" "0.00134990" "       741"
# [11,] "150" "0.00042906" "      2331"
# [12,] "155" "0.00012287" "      8139"
# [13,] "160" "0.00003167" "     31574"
# [14,] "165" "0.00000734" "    136176"
# [15,] "170" "0.00000153" "    653327"
# [16,] "175" "0.00000029" "   3488556"
# [17,] "180" "0.00000005" "  20741279"

• The probability of having an IQ of 180 or higher is 0.00000005.
• That's one in about 20 million. I.e., if the norm sample was Australia, he's either the smartest or one of the top few smartest people in Australia
• As for my thoughts on the final question: I think it's pretty low.