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    probability homework




    Hello, I am having difficulty figuring out my homework. I made attempts and could someone check my answers and see if I'm right or make suggestions? Thank you

    A physical-fitness association is including a mile run in its secondary-school fitness test for boys. The time for this event for boys in secondary school is approximately normally distributed with a mean of 450 seconds and a standard deviation of 40 seconds.

    a)What is the probability that a randomly selected boy takes between 420 and 540 seconds to run a mile?

    solution: normalcdf(420,540,450,40) = .761 = 76.1%

    b)What is the probability that a randomly selected boy takes at least 480 seconds to run a mile?

    solution: normalcdf(480,E99,450,40) = .227 = 22.7%

    c)What is the probability that a randomly selected boy takes at most 390 seconds to run a mile?

    solution: normalcdf(E99,390,450,40) = .0668 = 6.68%

    d)If the association wants to designate the fastest 20% as "above average, what time should the association set for this criterion?

    solution: please give me advice!

    e)If the association wants to designate the slowest 5% as "in need of medical evaluation," what time should the association set for this criterion?

    solution: please give me advice!


    Thank you in advance! I am trying!!

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    a) to c) is look fine.

    what s/w you are using? There must be some function for the inverse of the normal probabilities.

    d) we have to find value P[time < k seconds] = P[X< k] =.20

    e) P[X>k] =.05
    In the long run, we're all dead.

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    c)
    so you are saying to use the invnorm function?
    this is what i tried
    invNorm(.80,450,40) = 483.66 seconds
    is this correct?

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    it is d) I don't think that value make sense.
    Because fastest mean the lowest time.

    Try this.
    invNorm(.20,450,40)
    In the long run, we're all dead.

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    d)
    invNorm(.05,450,40)
    =384.206 seconds
    could this be it?

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    No. It is not correct. Do you think slowest and fastest can be identified using same strategy?

    Think practically about the values. like "slowest means 384 ? ". Since mean is 450 so it can't be slowest.
    This will help to avoid wrong answer.
    In the long run, we're all dead.

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    okay i tried invNorm(.20,450,40) = 416.335, is this the answer?

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    Quote Originally Posted by letsstophere View Post
    okay i tried invNorm(.20,450,40) = 416.335, is this the answer?
    seems fine.

    The above is d).


    Check your questions numbers again.
    In the long run, we're all dead.

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    As an incentive to improve the fitness of the secondary-school boys for a certain town, a rich benefactor offers a monetary prize to every student. Each student will earn P=640-X dollars, where X is their time in the mile run.

    a) What is the mean payout to a secondary-school boy (or, the mean of the random variable P)?

    solution: P = 640 - 450 = $190

    b) What are the variance and the standard deviations of the payout to a secondary-school boy (or, what are the variance and the standard deviations of the random variable P?)

    solution: advice needed.

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    b)

    Var(P) = Var(640-X)
    hint:
    Var( a+bX) = b^2*Var(X)
    In the long run, we're all dead.

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    i have no clue what you are trying to get me to do. thanks for helping

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    wait, i went back and did the first question and figured it out kind of
    e) for the slowest 5&#37;
    invnorm(.95,450,40) = 515.79 seconds

    d)the fastest 20%
    how would i figure this out?

  13. #13
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    in the variance what would be the "b"

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    ok i am being confusing i know sorry
    these are the answers i have so far
    1.
    a) 76.1%
    b) 22.7%
    c) 6.68%
    d) 416.34 seconds (fastest 20%, "above average are faster than 416.34)
    e) 515.79 seconds (slowest 5%, "in need of medical evaluation")

    2.
    a)P=640-450= $190
    b)i need to find the variance and standard deviation. please help

    and also check my answers! thanks!

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    Answers are correct.

    Regarding variance. I don't think hint will work for you.
    a and b are constant
    In your case b = -1 and a =640

    Var(640 - X ) = (-1)^2Var(X) = Var(X).=40^2
    I hope you know that standard deviation. = sqrt(Var)
    Last edited by vinux; 10-28-2008 at 04:39 PM.
    In the long run, we're all dead.

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