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# IQ IS NORMALLY DISTRIBUTED WITH A MEAN OF 100 AND A STANDARD

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Author: Christine Farr
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A) IQ is normally distributed with a mean of 100 and a standard deviation of 15.Suppose one individual is randomly chosen. Let X = IQ of an individual.1) Give the distribution of X.X ~ __ ( __, __)2) Find the probability that the person has an IQ greater than 115.3) Write the probability statement: P (____)4) What is the probability? (Round your answer to four decimal places.)5) Sketch the graph.6) Mensa is an organization whose members have the top 2% of all IQs. Find theminimum IQ needed to qualify for the Mensa organization.7) Write the probability statement: P(X > x) = ____8) What is the minimum IQ? (Round your answer to the nearest whole number.)x =__9) sketch the graph.10) The middle 60% of IQs fall between what two values?11) Write the probability statement: P(x1 < X < x2) =___12) State the two values. (Round your answers to the nearest whole number.)x1 =__x2 =__13) Sketch the graph.B) Suppose that the distance of fly balls hit to the outfield (in baseball) is normallydistributed with a mean of 200 feet and a standard deviation of 44 feet. Let X = distancein feet for a fly ball.1) Give the distribution of X; X ~__ (__,__)2) If one fly ball is randomly chosen from this distribution, what is the probability thatthis ball traveled fewer than 180 feet? (Round your answer to four decimal places.)3) Sketch the graph4) Find the 80th percentile of the distribution of fly balls in feet. (Round your answer toone decimal place.)5) Sketch the graph.Write the probability statement. (Let k represent the score that corresponds to the 80thpercentile.)P(X < k) =___C) Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that

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