The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): critical reading-502; mathematics-515; writing-494; Assume that the population standard deviation on each part of the test is = 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 (to 4 decimals)?

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20-06-2016
Mathematics

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The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): critical reading-502; mathematics-515; writing-494; Assume that the population standard deviation on each part of the test is = 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 (to 4 decimals)?

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Hussain514 Hussain514 · Answer 1 · 2016-07-03T03:10:19-04:00

AP(492 < x-bar < 512)

z = (492-502)/100/√90

z = -0.95 is 0.1711

z = (512-502)/100/√90

z = 0.95 is 0.8289

b. P(505 < x-bar < 525)

z = (505-515)/100/ √90

z = -0.95

z = (525-515)/100/ √90

z = 0.95

P(-0.95< z < 0.95) = 0.6578

P(-0.95< z < 0.95) = 0.6578

c. P(484 < x-bar < 504)

z = (484-494)/100/√100

z = -1 is 0.1587

z = (504-494)/100/√100

z = 1 is 0.8413

P(-1< z <1) = 0.6826