Question 259858
SAT verbal scores are normally distributed with mean of 450 and a standard deviation of 50.
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Note: I'll do A and D.  B and C are similar to A.
E is different so I'll do that.
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A. What percentage of students score less than 350?
Find the z-score of 350:
z(350)= (350-450)/50 = -100/50 = -2
P(x<350) = P(z<-2) = normalcdf(-100,-2) = 0.02275..
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B. What percentage of students score more than 400?
C. What percentage of students score less than 550?
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D. What percentage of students score between 350 and 550?
Find the z-score of 450:
z(450) = (450-450)/50 = 0
P(350 < x < 450) = P(-2< z < 0) = normalcdf(-2,0) = 0.4772...
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E. An Ivy League university only admits students who are in the top 2.5% of scores on this test. What minimum score should a student get on this test to get admitted into this university?
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Find the z-score that has a right-tail of 2.5%
That is invNorm(0.975) = 1.96
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Now use the formula x = z*sigma + u to find the corresponding x-score.
x = 1.96*50 + 450
x = 98 + 450
x = 548 (minimum score required to gain entrance to the university)
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Cheers,
Stan H.
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