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Math Help - Normal Distribution

  1. #1
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    Normal Distribution

    Hope some one can help me with this


    Let X1,X2 .... X16 be a random sample from a normal distribution N(77,25).

    Compute a)P(77<X<79.5)
    b) P(74.2<X<78.4)
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  2. #2
    Grand Panjandrum
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    Let X1,X2 .... X16 be a random sample from a normal distribution N(77,25).

    Compute a)P(77<X<79.5)
    b) P(74.2<X<78.4)
    What is X? the sample mean?

    RonL
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  3. #3
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    Yes -- it's actually X with a little line over the top- i didnt know how to put it in here.

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  4. #4
    Grand Panjandrum
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    Let X1,X2 .... X16 be a random sample from a normal distribution N(77,25).

    Compute a)P(77<X<79.5)
    b) P(74.2<X<78.4)
    The sample mean of a sample of size n from a normal distribution
    N(\mu,\sigma^2) has a normal distribution; N(\mu,\sigma^2/n).

    So in this case the SD of the sample mean is 5/4 so:

    <br />
P(77<X<79.5)=P(\bar X<X<\bar X + 2.5)= P(\bar X<X<\bar X + 2 \sigma)<br />
,

    Which may be looked up in a suitable table:

    <br />
P(77<X<79.5)=P(\bar X<X<\bar X + 2 \sigma)=0.4772<br />
.

    The second question is:

    <br />
P(74.2<X<78.4)=P(\bar X-2.8<X<\bar X + 1.4)= P(\bar X-2.24 \sigma <X<\bar X + 1.12 \sigma)<br />

    Which from tables I make 0.8686-0.0125=0.8561

    RonL
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