Question

A person must score in the upper of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. There are Mensa members in countries throughout the world (Mensa International website, January 8, 2013). If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?

Answer 1

The required IQ score a person must have to qualify for Mensa is 131

Explanation:

Here we have that to become a member requires scoring in the upper 2% of the population IQ

Therefore, we have P(z) = 0.98, From the the z table we have at 0.98 z = 2.054

Therefore, from

`z= \frac{ {x} - \mu}{\sigma}`

Where:

μ = Mean = 100

σ = Standard deviation = 15

x = Required IQ score

2.054×15 = x - 100

30.81 = x - 100

x = 100 + 30.81 = 130.81 ≈ 131

Therefore, the IQ score of the person must be 131 and above to qualify for Mensa.