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In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25....

  1. In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. What are the mean and standard deviation of the sample mean IQ? What is the shape of the distribution?
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Answer #1

E(Xbar) = E(X) = 112

sd(Xbar) = sd(X)/sqrt(n) = 25/sqrt(300) = 1.44337

Xbar follow N(112,25^2/300)

shape is bell-shaped

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