Question 259858: Sat verbal scores are normally distributed whith mean of 450 and a standard deviation of 50.
A. What percentage of students score less than 350?
B. What percentage of students score more than 400?
C. What percentage of students score less than 550?
D. What percentage of students score between 350 and 550?
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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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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