Solve IQ Test Problem: Percent Adults Qualifying for MENSA Membership

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SUMMARY

The discussion centers on calculating the percentage of adults qualifying for MENSA membership based on IQ scores. Given a normal distribution with a mean of 100 and a standard deviation of 15, MENSA requires a minimum IQ score of 130. To find the qualifying percentage, participants suggest using the Z-score formula, Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. The 68-95-99.7 rule is referenced as a method to understand the distribution of scores.

PREREQUISITES
  • Understanding of normal distribution and its properties
  • Familiarity with the Z-score formula
  • Knowledge of the 68-95-99.7 rule
  • Basic statistics concepts
NEXT STEPS
  • Calculate Z-scores for various IQ thresholds using the formula Z = (X - μ) / σ
  • Research the application of the 68-95-99.7 rule in real-world scenarios
  • Explore statistical software tools for normal distribution analysis
  • Learn about percentile ranks and their significance in IQ testing
USEFUL FOR

Statisticians, educators, psychologists, and anyone interested in understanding IQ distributions and membership qualifications for high-IQ societies like MENSA.

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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