3. During a study of the IQ of Idahoans, researchers find that all scores have a

Question

3. During a study of the IQ of Idahoans, researchers find that all scores have a bell shaped distribution with mean IQ of 125 and variance 256. Using the empirical rule draw the relative frequency distribution for IQ scores in Idaho. a) Using either your diagram, tables on the handout or Chebyshev's theorem what percentage of the Idahoans will have IQ's between 109 and 141 b) What is the percentage of folks with IQ's below 97? c) My friend Paul from Pocatello has an IQ of 137. Calculate Paul's z-score and determine if he is a genius

Explanation / Answer

(a) Here as per empirical rule of 68 - 95 - 99.7

Mean = 125

standard deviation = sqrt (256) = 16

Pr(109 < x < 141) = Pr(125 - 16 < X< 125 + 16) = 0.6827

(b) Pr(x < 97)

Z = (97 - 125)/16 = -1.75

Pr(x < 97) = Pr(Z < -1.75) = 0.04

so 4% probability that IQ is below 97

(c) Z = (137 - 125)/16 = 0.75

Percentile score = Pr(Z < 0.75) = 0.7734 so77.34% percentile not in top 10% so can't be called genius.

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