Question

A genius society requires an IQ that is in the top 2% of the population in order to join. If an IQ test has a mean of 100 and a standard deviation of 15, which of the following could be used as the minimum qualifying score to join the genius society? 115 130 145 160.

Answer 1

The minimum score to join the genius society is 130.

What is the probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given

A genius society requires an IQ that is in the top 2% of the population in order to join.

If an IQ test has a mean of 100 and a standard deviation of 15.

The top 2%, you have to have an IQ higher than 98% of the population (100% - 2%).

This is also known as the 98th percentile.

For this problem, you are given the probability and need to determine the raw score.

The closest probability is 0.97982 and that corresponds to a z-score of 2.05.

$\rm z - score=\dfrac{x-mean}{standard \ deviatiion}\\\\2.05=\dfrac{x-100}{15}\\\\x-100=15\times 2.05\\\\x-100=30.75\\\\x=100+30.75\\\\x=130.75$

Hence, the minimum score to join the genius society is 130.

To know more about probability click the link given below.

brainly.com/question/743546