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Math Help - Mathematical statistic? Random variable, normal distribution, standard deviation?

  1. #1
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    Mathematical statistic? Random variable, normal distribution, standard deviation?

    Say X a random variable that satisfies a normal distribution


    E(X) = 15, the standard deviation is 3.

    1) Write down the density function of X.
    y = e^(−(x−15)/3) / √[ 2π3 ]
    y = e^(−(x−15)/18) / √[ 18π ]

    2) Compute P(X <= 18)
    18 − 15 = 3
    3 / 3 = 1
    P(Z<1) = 84.13%

    3) Compute P(X >= 21)
    P(X>21)
    21 − 15 = 6
    6 / 3 = 2
    P(Z>2) = 2.27%

    4) Compute P(11 <= X <= 19)
    P(11<X<19)
    11 − 15 = −4
    Z₂ = −4 / 3 = −1.333
    19 − 15 = 4
    Z₁ = 4 / 3 = 1.333
    P(−1.333<Z<1.333) = 81.75%

    Can someone verified if these are 100% correct? Thanks, you need a table for this problem though.
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  2. #2
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    Quote Originally Posted by dkmathguy View Post
    Say X a random variable that satisfies a normal distribution


    E(X) = 15, the standard deviation is 3.

    1) Write down the density function of X.
    y = e^(−(x−15)/3) / √[ 2π3 ]
    y = e^(−(x−15)/18) / √[ 18π ]

    2) Compute P(X <= 18)
    18 − 15 = 3
    3 / 3 = 1
    P(Z<1) = 84.13%

    3) Compute P(X >= 21)
    P(X>21)
    21 − 15 = 6
    6 / 3 = 2
    P(Z>2) = 2.27%

    4) Compute P(11 <= X <= 19)
    P(11<X<19)
    11 − 15 = −4
    Z₂ = −4 / 3 = −1.333
    19 − 15 = 4
    Z₁ = 4 / 3 = 1.333
    P(−1.333<Z<1.333) = 81.75%

    Can someone verified if these are 100% correct? Thanks, you need a table for this problem though.
    I cannot stand answers to questions like these expressed as a percentage. You should be giving a number correct to four decimal places that lies between 0 and 1.

    Having said this, your answers are correct (taken with a grain of salt), except:

    I get 0.0228 for #3, correct to four decimal places (which I suppose you would want to write as 22.28% ....).
    I get 0.8176 for #4, correct to four decimal places (which I suppose you would want to write as 81.76% ....).
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  3. #3
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    Thanks mr fantastic for verifying this. I will write my answer to 4 decimal places form now on.
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