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STAT 250 Section 001 Quiz #4 Spring 1998 Name ______________________________ Student ID __________________________ Stanford-Binet IQ scores are known to follow a normal distribution with mean 100 and standard deviation 16. Recall Z = (X µ)/) and X=µ + Z). 1. (2 points) What is the probability that a randomly selected individual has an IQ score above 128? P(X > 128) = P(Z > (128100)/16) = P(Z > 1.75) = 1 0.9599 = 0.0401 That is, only 4.01% of the population has an IQ above 128. 2. (2 points) Mensa is an organization that only allows people to join if their IQs are in the top 2% of the population. What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa? Z for 98th percentile is 2.05 So X = µ + Z) = 100 + 2.05(16) = 132.8 That is, only 2% of the population has an IQ above 132.8. 3. (1 point) The normal probability rule tells that 95% of the population have IQ scores between what two numbers? The normal probability rule tells us that 95% of the people have IQ scores between µ2) and µ+2), or between 1002(16) and 100+2(16), i.e. between 68 and 132.