IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an international society that has one and only one qualification for membership: a score in the top 2% on an IQ test. a. What IQ score should one have in order to be eligible for Mensa

130.81

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ,

where from the question:

x is the raw score = ?

μ is the population mean = 100

σ is the population standard deviation = 15

We are told in the question that:

Mensa is an international society that has one and only one qualification for membership: a score in the top 2% on an IQ test.

The top 2% means a score in the 98th percentile

The z score of the 98th percentile = 2.054

Hence:

2.054 = x - 100/15

Cross Multiply

2.054 × 15 = x - 100

30.81 = x - 100

x = 30.81 + 100

x = 130.81

The IQ score that one should have in order to be eligible for Mensa is the score of 130.81