Mensa is an organization that allows people to join only if their IQs are in the top 2% of the population What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa?

Question

(Remember that the mean is 100 and the standard deviation is 15)

Mensa also allows members to qualify on the basis of certain standard tests. If you were to try to qualify on the basis of the quantitative reasoning part of the GRE exam, what score would you need on the exam? (Remember that the mean is 151.3 and the standard deviation is 8.7)

Answer 1

First find z that corresponds to 98th percentile (probability = 0.98) which is z = 2.054

Let x = IQ

z = (x - mean)/SD

using given mean 100, SD = 15 and z = 2.054, substitute in to above equation and solve for x:

2.054 = (x - 100)/15

x = 2.054 * 15 + 100 = 130.81

For second question what percentile is considered passing?