Answer:
130.81
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