Math

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 = 100.

a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)?

b. What is the probability a 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)?

c. What is the probability a 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 (to 4 decimals)?

  1. 👍 2
  2. 👎 0
  3. 👁 6,991
  1. a. P(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

    1. 👍 3
    2. 👎 3
  2. a. P(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

    P(-0.95< z < 0.95) = 0.6578

    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

    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

    1. 👍 6
    2. 👎 1
  3. Yall are wrong

    1. 👍 1
    2. 👎 1

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