SOLUTION: The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Assume that the population standard devi

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Question 526304: The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):
Assume that the population standard deviation on each part of the test is σ = 100.
What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Round your answer to four decimal places.
What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Round your answer to three decimal places.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):
Assume that the population standard deviation on each part
of the test is σ = 100.
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What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Round your answer to four decimal places.
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Find the z-values 5% to the right and 5% to the left of z = 0.
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invNorm(0.45) = -0.1257
invNorm(0.55) = +0.1257
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Find the corresponding raw scores using x = zs+u
x = -0.1257*100+515 = 502.4339
and
x = +0.1257*100+515 = 525.5700
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What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Round your answer to three decimal places.
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I'll do part of this one; you can do the rest.
5 below 494 = 489
std for the sample means of size n = 100 is 100/Sqrt(100) = 10
z(489) = (489-494)/10 = -1/2
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Similarly the z-score above 494 will be +1/2
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Then P(489 <= x-bar <= 499) = P(-1/2<= z <=1/2) = 0.3829
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Cheers,
Stan H.
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