Results 1 to 8 of 8

Math Help - Prob Dist.. just some clarity please.

  1. #1
    Junior Member
    Joined
    Jan 2006
    Posts
    29

    Prob Dist.. just some clarity please.

    could somebody do question b
    Attached Thumbnails Attached Thumbnails Prob Dist.. just some clarity please.-question.jpg  
    Last edited by Arbitur; April 26th 2006 at 08:51 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jan 2006
    Posts
    29
    changed the question
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Arbitur
    could somebody do question b
    b) Probability of 3 or more blue in 4 trials.

    Probability of a blue on any trial is 0.8 as we are sampling with replacement,
    so:

    <br />
P(N_{blue} \ge 3)=P(N_{blue} = 3)+P(N_{blue} = 4)<br />

    but:

    <br />
P(N_{blue} = K\ \mbox{in M trials})={M \choose K}p^K(1-p)^{M-K}= \frac{M!}{K!(M-K)!}p^K(1-p)^{M-K}<br /> <br />

    Here p=0.8, so:

    <br />
P(N_{blue} \ge 3)=\frac{4!}{3!1!}\ 0.8^3\ 0.2^1+\frac{4!}{4!0!}\ 0.8^4\  0.2^0<br />

    Which since 1!=0!=1 may be reduced to:

    <br />
P(N_{blue} \ge 3)=4\ 0.8^3\ 0.2+0.8^4<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2006
    Posts
    29
    uhm can you explain that in words?
    i need to get it to a percent number
    i thought it had to be something like
    mean=.8*4-3.2
    standard deviation=square root of 4*.8*.2
    =.64

    so (SOME NUMBER)-3.2/.64 =the zscore i need to get the percentage???
    that is what my book is teaching me
    what number do i use
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Arbitur
    uhm can you explain that in words?
    i need to get it to a percent number
    i thought it had to be something like
    mean=.8*4-3.2
    standard deviation=square root of 4*.8*.2
    =.64

    so (SOME NUMBER)-3.2/.64 =the zscore i need to get the percentage???
    that is what my book is teaching me
    Then you are probably looking at the wrong section of your book. You
    should be looking at the section that deals with the Binomial distribution.


    what number do i use
    See the last line of my post:

    <br />
P(N_{blue} \ge 3)=4\ 0.8^3\ 0.2+0.8^4<br />

    That can be simplified to the number you want:

    <br />
P(N_{blue} \ge 3)=4\ 0.8^3\ 0.2+0.8^4\approx 0.819<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jan 2006
    Posts
    29
    thanks anyways but i have no idea how u get that ;/
    ok im looking through my book and
    because of a rule i cant use the z-score way and crap... but how do i know what way and numbers to use then

    ok i get it now... but what if b used really big numbers... would it still work that easy? if not what would i do( cause those are easily added 2 gether)
    Last edited by Arbitur; April 26th 2006 at 09:48 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Arbitur
    thanks anyways but i have no idea how u get that ;/
    ok im looking through my book and
    because of a rule i cant use the z-score way and crap... but how do i know what way and numbers to use then

    ok i get it now... but what if b used really big numbers... would it still work that easy? if not what would i do( cause those are easily added 2 gether)
    With really "big numbers" you would use the normal approximation to the
    binomial distribution; see this thread

    RonL
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by CaptainBlack
    With really "big numbers" you would use the normal approximation to the
    binomial distribution; see this thread

    RonL
    That the normal approximation is not too good for small problem sizes can
    be shown by reworking this problem using the normal approximation.

    Here p=0.8, and N=4, so the mean number
    of blues is:

    <br />
\mu_B=0.8 \times 4=3.2<br />

    The vaiance of the number of blues is:

    <br />
\sigma_B^2=4\times 0.8 \times 0.2=0.64<br />

    Now we want the probability of 3 or more blues, so we want
    the critical z-score for 2.5 (rounding down by 0.5
    as a continuity correction):

    <br />
z_{critical}=\frac{2.5-3.2}{0.8}=-0.875<br />
,

    Look this up in a normal table we find:

    <br />
P(z>-0.875)\approx 0.809<br />

    rather than the correct value of \sim 0.819

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 29th 2010, 05:07 AM
  2. Replies: 4
    Last Post: December 10th 2009, 05:57 AM
  3. Just for a little clarity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 16th 2009, 04:48 AM
  4. HEP ME>>>> Prob Dist
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 4th 2008, 08:23 PM
  5. Normal Dist Prob
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 4th 2007, 05:25 AM

Search Tags


/mathhelpforum @mathhelpforum