Results 1 to 4 of 4

Math Help - Help with one short problem.

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    2

    Help with one short problem.

    1.The driving time for an individual from his home to his work is distributed between 300 to 480 seconds.
    So here are the two things I need to solve for this problem:

    Compute the probability that the driving time will be less than or equal to 435 seconds.
    Determine the expected driving time and its standard deviation.



    How can I do this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Math123 View Post
    1.The driving time for an individual from his home to his work is distributed between 300 to 480 seconds.
    So here are the two things I need to solve for this problem:

    Compute the probability that the driving time will be less than or equal to 435 seconds.
    Determine the expected driving time and its standard deviation.



    How can I do this?
    First as you have typed the question there is no answer as you have not specified a distribution. But lets assume you mean uniformly distributed between 300 and 480 seconds.

    Probability that travelling time is less than 435 is:

    integral (p(x) dx, x=-inf,435) = integral (1/180) dx, x=300,435)

    as p(x)=(1/180) for x in (300, 480), and 0 otherwise.

    integral (p(x) dx, x=-inf, 435) = integral (1/180) dx, x=300, 435)
    ............................. ..=(1/180) (435-300)=135/180 = 0.75



    By definition the mean:

    m = integral (x p(x) dx, x=-inf, inf) = integral (x/180 dx, x=300, 480)
    .............................. ........=480^2/360-300^2/360 = 390.



    The definition of SD:

    s = sqrt(V),

    V = integral ((x-m)^2 p(x) dx, x=-inf, inf)

    which I will leave for you to do.

    RonL
    Last edited by CaptainBlack; February 18th 2007 at 10:46 PM. Reason: improve formating
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2007
    Posts
    2
    I'm not getting it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Math123 View Post
    I'm not getting it.
    The uniform distribution between 300 and 480 has density:

    p(x)=(1/180); x in (300, 480)
    p(x)=0 otherwise.

    Then you just use the text book definitions of the quatities you require
    and compute the integrals.

    p(x<a) = integral p(x) dx, x=-inf, a

    mu= integral xp(x) dx, x=-inf, inf

    var= integral (x-mu)^2 p(x) dx, x=-inf, inf

    sigma=sqrt(var)

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. short money word problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 30th 2010, 11:24 AM
  2. Short maths problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 12th 2009, 03:05 AM
  3. Easy (and short) problem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 10th 2009, 12:18 AM
  4. Short Calculus Problem!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 13th 2006, 07:58 PM
  5. A short problem, help me please!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 5th 2006, 03:13 PM

Search Tags


/mathhelpforum @mathhelpforum