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Math Help - Help with Z scores and probabilities....

  1. #1
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    Question Help with Z scores and probabilities....

    A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ________% of minority students.

    Answer Key: 49.83


    Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000? For calculations, use your book table E.2.

    Answer Key: 0.4532

    I need to know how do to solve these. The answers have been given but i need to know how they got those asnwers.

    For the first problem I think i need to figure the standard dev

    I know for the second problem i need to use a z score but i dont know how to figure out the sample and population mean from the info given.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Blevil View Post
    A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ________% of minority students.

    Answer Key: 49.83
    The number of minority students in a sample of 75 has a binomial distribution with mean 0.45 \times 75 and a standard deviation \sqrt{75 \times 0.45 \times 0.55}.

    Now assume that the sample sizes are sufficient to use the normal approximation with the above mean and standard deviation.

    CB
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  3. #3
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    Thanks CaptainBlack

    Im still not getting the answer I have ((75*.8)-(75*.45))/sqrt(75*.45*.55) <<< where am i going wrong?
    Last edited by Blevil; July 14th 2010 at 02:45 PM.
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  4. #4
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    Try this:

    .845 = (x - 75*.45)/sqrt(75*.45*.55)

    Once you solve for x you need to divide by the sample size of 75 to put it in % of minority students as the problem asks. The .845 on the left hand side of the equation comes from standard normal distribution corresponding to 80%.
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  5. #5
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    .845 = (x - 75*.45)/sqrt(75*.45*.55)

    ok so .845^2 = (x - 75*.45)/(75*.45*.55)

    (.845^2)*(75*.45*.55)=(x - 75*.45)

    so (.845^2)*(75*.45*.55) + (75*.45) = X << is this correct because i come with some weird number like 45.00 or something....darn im still stumped
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