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Math Help - normal distribution -help!

  1. #1
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    Post normal distribution -help!

    In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and S.D. of the distribution.

    I need some help on the above number. Thanx.
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  2. #2
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    Quote Originally Posted by okello View Post
    In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and S.D. of the distribution.

    I need some help on the above number. Thanx.
    \Pr(X < 45) = 0.31.

    Find the value a of Z such that \Pr(Z < a) = 0.31.

    From Z = \frac{X - \mu}{\sigma} it follows that a = \frac{45 - \mu}{\sigma}.

    Substitute your value of a to get equation (1) with the unknowns \mu and \sigma.


    \Pr(X > 64) = 0.08.

    Find the value b of Z such that \Pr(Z > b) = 0.08.

    From Z = \frac{X - \mu}{\sigma} it follows that b = \frac{64 - \mu}{\sigma}.

    Substitute your value of b to get equation (2) with the unknowns \mu and \sigma.


    Solve equations (1) and (2) simultaneously.
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    Smile normal distribution - help!

    Hi Mr. Fantastic, thanx.

    I got as -82.6 and as 70.6 using a calculator.

    Kindly confirm. Thanks once again.

    Regards,
    Okello
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  4. #4
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    Quote Originally Posted by okello View Post
    Hi Mr. Fantastic, thanx.

    I got as -82.6 and as 70.6 using a calculator.

    Kindly confirm. Thanks once again.

    Regards,
    Okello
    I doubt \sigma is correct - for starters you have it negative!! Even ignoring the -ve as a typo it's size is way too big.

    If you post your calculations I will review them for the mistake(s) (but be patient because I'm very busy and might take some time to post).
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  5. #5
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    Post normal distribution - help!

    Hi Mr. Fantastic,
    I made = 0.31 ..............(i)

    and =0.08 ...................(ii)

    implying that

    0.31 + = 45 -----iii
    0.08 + = 64 ------iv

    And used calc to find 2 unknowns. And I got as -82.6 and as 70.6 using a calculator.

    Await for your response.
    Thanks
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  6. #6
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    Quote Originally Posted by okello View Post
    Hi Mr. Fantastic,
    I made = 0.31 ..............(i)

    and =0.08 ...................(ii)

    implying that

    0.31 + = 45 -----iii
    0.08 + = 64 ------iv

    And used calc to find 2 unknowns. And I got as -82.6 and as 70.6 using a calculator.

    Await for your response.
    Thanks
    Quote Originally Posted by mr fantastic View Post
    \Pr(X < 45) = 0.31.

    Find the value a of Z such that \Pr(Z < a) = 0.31.

    Mr F adds: This does NOT mean that a = 0.31.

    [snip]

    \Pr(X > 64) = 0.08.

    Find the value b of Z such that \Pr(Z > b) = 0.08.

    Mr F adds: This does NOT mean that b = 008.

    [snip]
    If \Pr(Z < a) = 0.31 then you're expected to be able to get (using tables or technology) that a = -0.4959 since \Pr(Z < -0.4959) = 0.31

    Similar with b.

    This is the inverse normal problem - you must have met questions like this in your earlier work ....
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  7. #7
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by okello View Post
    Hi Mr. Fantastic, thanx.

    I got as -82.6 and as 70.6 using a calculator.

    Kindly confirm. Thanks once again.

    Regards,
    Okello

    A negative standard deviation?
    This is why I don't like seeing calculators in my class, especially integral calculators.
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  8. #8
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    Post normal distribution - help!

    Hi Matheagle,
    Have you calculated it?. What answer did you get?

    Regards,
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  9. #9
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    Quote Originally Posted by okello View Post
    Hi Matheagle,
    Have you calculated it?. What answer did you get?

    Regards,
    Wrong questions.

    Here are the correct questions:

    Hi okello,
    Have you calculated b? What answer did you get?
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  10. #10
    MHF Contributor matheagle's Avatar
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    I'm going to put a similar problem on my exam next week.
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