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The distribution of scores on the SAT is approximately normal with a mean of 500 and a standard deviation of 100. For the population of students who have taken the SAT, what proportion have a sat score less than 400?

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[tex]\mathbb P(X<400)=\mathbb P\left(\dfrac{X-500}{100}<\dfrac{400-500}{100}\right)=\mathbb P(Z<-1)\approx0.1587[/tex]

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