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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Intelligence Quotient (IQ) scores are
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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