Intelligence Quotient (IQ) scores are normally distributed with a mean of 100 and a standard deviation of 15. i. To qualify for membership of Mensa, the organization for the “intellectually very superior”, one requires an IQ score above 131.5. What percentage of people meet the Mensa eligibility requirement?  ii. If we redefine the category of ‘intellectually very superior” to be scores in the top 2.28 %, what does the minimum score now become for Mensa membership eligibility?  iii. If 25 people are randomly selected for an IQ test, find the probability that their mean IQ score is between 95 and 105.

Question

Intelligence Quotient (IQ) scores are normally distributed with a mean of 100 and
a standard deviation of 15.
i. To qualify for membership of Mensa, the organization for the “intellectually
very superior”, one requires an IQ score above 131.5. What percentage of
people meet the Mensa eligibility requirement? 
ii. If we redefine the category of ‘intellectually very superior” to be scores in
the top 2.28 %, what does the minimum score now become for Mensa
membership eligibility? 
iii. If 25 people are randomly selected for an IQ test, find the probability that
their mean IQ score is between 95 and 105.

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