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Math Help - Normal Distribution Problem (Attempted Working Inside)

  1. #1
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    Talking Normal Distribution Problem (Attempted Working Inside)

    X~N(8,25)
    P( {-a}\leq X \leq{a})=0.4

    We need to find a.

    I decided to use GC and standardize it to find a.
    P( {(-a-8)/5}\leq {Z} \leq{(a-8)/5})=0.4
    Since it is now standardized,

    P( {(-a-8)/5}\leq {Z} \leq{(a-8)/5})
    =1-2P( {Z}\geq{(a-8)/5})=0.4
    P( {Z}\geq{(a-8)/5})=0.3
    P( {Z}\leq{(a-8)/5})=0.7

    So I used Ti84 InvNorm Function to get {(a-8)/5}=0.5244
    Which means {a} is 10.622. However, the ans is 6.75.

    Anyone can point out my mistake?

    Thanks.
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  2. #2
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    Quote Originally Posted by qazxsw11111 View Post
    X~N(8,25)
    P( {-a}\leq X \leq{a})=0.4

    We need to find a.

    I decided to use GC and standardize it to find a.
    P( {(-a-8)/5}\leq {Z} \leq{(a-8)/5})=0.4
    Since it is now standardized,

    P( {(-a-8)/5}\leq {Z} \leq{(a-8)/5})
    =1-2P( {Z}\geq{(a-8)/5})=0.4
    P( {Z}\geq{(a-8)/5})=0.3
    P( {Z}\leq{(a-8)/5})=0.7

    So I used Ti84 InvNorm Function to get {(a-8)/5}=0.5244
    Which means {a} is 10.622. However, the ans is 6.75.

    Anyone can point out my mistake?

    Thanks.
    Your mistake is in believing that your answer is wrong and that 6.75 is correct.

    Substitute a = 10.622 and use your TI-89 to confirm your answer.
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