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Math Help - for a standard normal random variable

  1. #1
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    for a standard normal random variable

    a) find P(-.12<Z<.54)

    b)find P(z=0)

    c) find the z-score that seperates the bottom 40% frin the top 60%

    D) find the z-scores for which 95 % of the distribution is between -z and z

    If you are able to help me I want to thank you in advance
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  2. #2
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    Quote Originally Posted by stewardt View Post
    a) find P(-.12<Z<.54)

    Mr F says: = Pr(Z < 0.54) - Pr(Z < - 0.12) = Pr(Z < 0.54) - Pr(Z > 0.12) = Pr(Z < 0.54) - [1 - Pr(Z < 0.12)] = Pr(Z < 0.54) + Pr(Z < 0.12) - 1.

    Now use your tables.

    b)find P(z=0) Mr F says: You should know that since Z is a continuous random variable, Pr(Z = a) = 0.

    c) find the z-score that seperates the bottom 40% frin the top 60%

    Mr F says: Pr(Z < - z*) = 0.4 => Pr(Z > z*) = 0.4 => Pr(Z < z*) = 0.6. Get z* by using your tables in a reverse way. Hence get -z*.

    D) find the z-scores for which 95 % of the distribution is between -z and z

    Mr F says: Pr(Z > z) = 0.025 => Pr(Z < z) = 0.975. Get z by using your tables in a reverse way.

    If you are able to help me I want to thank you in advance
    If you can help me more on a one on one basis then tell me so
    let me know how much you would charge to help me
    ..
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  3. #3
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    im still confused

    Mr F says: = Pr(Z < 0.54) - Pr(Z < - 0.12) = Pr(Z < 0.54) - Pr(Z > 0.12) = Pr(Z < 0.54) - [1 - Pr(Z < 0.12)] = Pr(Z < 0.54) + Pr(Z < 0.12) - 1.
    do I look at the table where -1 is
    Mr F says: Pr(Z < - z*) = 0.4 => Pr(Z > z*) = 0.4 => Pr(Z < z*) = 0.6. Get z* by using your tables in a reverse way. Hence get -z*.
    are you saying here 1-.xxxx
    Mr F says: Pr(Z > z) = 0.025 => Pr(Z < z) = 0.975. Get z by using your tables in a reverse way.
    I have no idea what to do
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  4. #4
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    Quote Originally Posted by stewardt View Post
    im still confused

    Mr F says: = Pr(Z < 0.54) - Pr(Z < - 0.12) = Pr(Z < 0.54) - Pr(Z > 0.12) = Pr(Z < 0.54) - [1 - Pr(Z < 0.12)] = Pr(Z < 0.54) + Pr(Z < 0.12) - 1.
    do I look at the table where -1 is

    Mr F says: No. You use your tables to look up Pr(Z < 0.54) and Pr(Z < 0.12).

    Mr F says: Pr(Z < - z*) = 0.4 => Pr(Z > z*) = 0.4 => Pr(Z < z*) = 0.6. Get z* by using your tables in a reverse way. Hence get -z*.
    are you saying here 1-.xxxx

    Mr F says: No. I'm saying go to the main body of your tables and find 0.6. Then work backwards from it to find what the value of z is.

    Mr F says: Pr(Z > z) = 0.025 => Pr(Z < z) = 0.975. Get z by using your tables in a reverse way.
    I have no idea what to do

    Mr F says: If that's true then you're strongly advised to seek urgent help from your teacher.

    Go to the main body of your tables and find 0.975. Then work backwards from it to find what the value of z is.
    ..
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    ..
    D) find the z-scores for which 95 % of the distribution is between -z and z

    Mr F says: Pr(Z > z) = 0.025 => Pr(Z < z) = 0.975. Get z by using your tables in a reverse way.

    the answer to this question is 1.96 then
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  6. #6
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    Quote Originally Posted by stewardt View Post
    D) find the z-scores for which 95 % of the distribution is between -z and z

    Mr F says: Pr(Z > z) = 0.025 => Pr(Z < z) = 0.975. Get z by using your tables in a reverse way.

    the answer to this question is 1.96 then
    Yes, z = 1.96 (correct to two decimal places)
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    Yes, z = 1.96 (correct to two decimal places)
    find the z-score that corresponds to the third quartile Q3
    is it .7486
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  8. #8
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    Quote Originally Posted by stewardt View Post
    find the z-score that corresponds to the third quartile Q3
    is it .7486
    No. Pr(Z > z*) = 0.25 => Pr(Z < z*) = 0.75 => z* = 0.6745 (correct to four decimal places).

    And new questions should be asked in a new thread.
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