Solve IQ Test Problem: Percent Adults Qualifying for MENSA Membership

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Discussion Overview

The discussion revolves around a problem related to calculating the percentage of adults qualifying for MENSA membership based on IQ scores, which are normally distributed with a mean of 100 and a standard deviation of 15. The focus is on understanding how to apply the normal distribution and the 68-95-99.7 rule in this context.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • Some participants express confusion about how to begin solving the problem, specifically regarding the application of the 68-95-99.7 rule.
  • One participant suggests that standardization is necessary, indicating the formula Z = (X - μ) / σ as a method to convert the IQ score to a standard score.
  • Another participant reiterates the need for standardization and clarifies the formula used for this process.

Areas of Agreement / Disagreement

There is no consensus on the approach to solving the problem, as some participants are still seeking clarification on the initial steps, while others have proposed standardization as a necessary step.

Contextual Notes

Participants have not fully explored the implications of the 68-95-99.7 rule in this specific context, and there may be assumptions about familiarity with standardization that are not explicitly stated.

alandry06
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The problem goes as such;

The scale of scores on an IQ test is approximately Normal with mean 100 and standard deviation 15. The organization MENSA, which calls itself "the high-IQ society," requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?


I know I can use the 68-95-99.7 rule, but I am confused at where to begin.
 
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Wrong section, sorry.
 
alandry06 said:
The problem goes as such;

The scale of scores on an IQ test is approximately Normal with mean 100 and standard deviation 15. The organization MENSA, which calls itself "the high-IQ society," requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?


I know I can use the 68-95-99.7 rule, but I am confused at where to begin.
Can you state the the 68-95-99.7 rule?
 
You have to standardize first, using Z=X-\mu/\sigma
 
Lateral said:
You have to standardize first, using Z =
(X-\mu)/\sigma is what you must have meant.
 

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