Question

A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 10, what score must a person have to qualify for Mensa?

Answer 1

Solution :

Given that,  

mean = = 100

standard deviation = = 10

Using standard normal table ,

P(Z > z) = 2%

1 - P(Z < z) = 0.02

P(Z < z) = 1 - 0.02 = 0.98

P(Z < 2.05) = 0.98

z = 2.05

Using z-score formula,

x = z * +

x = 2.05 * 10 + 100 = 120.50

score must a person have to qualify for Mensa is 120.50