Results 1 to 5 of 5

Math Help - Normal probability distributions

  1. #1
    Newbie
    Joined
    May 2007
    Posts
    8

    Normal probability distributions

    assume that men's weight are normaly distributed with mean 172 lb and a standard deviation 29 lb
    If 100 men are randomly selected find the probability that weight of 10 of them is less than 150 lb and weight of
    the remaining 90 of them is more or equal to 150 lb.
    I'm lost.
    I'l be very appreciate if somebody helps me.
    Last edited by CaptainBlack; May 13th 2007 at 01:55 AM. Reason: correct the question
    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 busyboy View Post
    assume that men's weight are normaly distributed with mean 172 lb and a standard deviation 29 lb
    If 100 men are randomly selected find the probability that weight of 10 of them is less than 150 lb and weight of them is more or equal to 150 lb.
    I'm lost.
    I'l be very appreciate if somebody helps me.
    The distribution of the mean of a sample of size n from a normal distribution
    with mean mu and SD sigma, has mean m=mu and SD sm=sigma/sqrt(n).

    So in this case the mean of the sample of 10 has mean 172 lb and SD 29/sqrt(10) ~= 9.17 lb.

    Now the z score of a mean of 150 lb is:

    z = (150 - m)/sm = (150 - 172)/9.17 ~= -2.40

    Now we look this z-score up in a table of the cumulative standard normal distribution to
    get the probability of observing a z-score this low or lower. Doing this we find the probability
    is 0.0082 (0.82%), which is also the probability that the mean weight of 10 of the men is <= 150 lb.

    The probability that the mean weight of a sample of 90 of the men is >150lb is derived
    by observing for a sample of 90 the SD of the mean is sm = sigma/sqrt(90) = 29/sqrt(90) =3.06.
    So the z-score is now:

    z = (150 - m)/sm = (150 - 172)/3.06 ~= -7.19

    and there is no need to look this up the required probability is so close to 1 that my tables
    do not go that far.

    RonL
    Last edited by CaptainBlack; May 13th 2007 at 01:59 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2007
    Posts
    8

    Smile

    Thank you very much for you help!
    Why did you not use number 100 anywere ?
    I am not sure,but I think that probability will depend from amount men which randomly selected .
    Sincerely, Busyboy.
    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 busyboy View Post
    Thank you very much for you help!
    Why did you not use number 100 anywere ?
    I am not sure,but I think that probability will depend from amount men which randomly selected .
    Sincerely, Busyboy.
    Because that was just misdirection, the question was really about one sample
    of 10 and another of 90.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2007
    Posts
    8

    Smile

    I'm VERY appreciate you for your explanation!!!
    Thanks a lot!!!!!
    Busyboy.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Normal Probability Distributions....
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 29th 2011, 06:04 AM
  2. normal distributions/probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 18th 2010, 07:37 AM
  3. normal probability distributions
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 25th 2009, 07:52 PM
  4. Stats Questions: Probability and Normal Distributions
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: December 15th 2008, 10:10 PM
  5. Conditional probability with normal distributions
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 22nd 2008, 04:13 AM

Search Tags


/mathhelpforum @mathhelpforum