Results 1 to 2 of 2

Thread: standard normal

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    139

    standard normal

    Let X follow a normal distribution
    mean=80 and Var=100

    the probability is 0.08 that X is in the symmetric interval about the mean between which two numbers?


    I did:

    P( a <x< b)= .08
    a= mean - k
    b= mean + k

    P( -k/stand dev < Z< k/st dev) =.08
    F(k/st dev)- F(-k/st dev) =.08
    F(k/st dev) - [ 1- F(k/ st dev)]= 0.08
    2F(k/st dev)=1.08 from which k= 1 and a= 79

    but the result on the book is a= 62.5

    Help me, please. Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by 0123 View Post
    Let X follow a normal distribution
    mean=80 and Var=100

    the probability is 0.08 that X is in the symmetric interval about the mean between which two numbers?


    I did:

    P( a <x< b)= .08
    a= mean - k
    b= mean + k

    P( -k/stand dev < Z< k/st dev) =.08
    F(k/st dev)- F(-k/st dev) =.08
    F(k/st dev) - [ 1- F(k/ st dev)]= 0.08
    2F(k/st dev)=1.08 from which k= 1 and a= 79

    but the result on the book is a= 62.5

    Help me, please. Thank you
    $\displaystyle X$ is $\displaystyle N(80 , 100)$ and $\displaystyle Z = \frac{X - 80}{10}$

    so if $\displaystyle P(80-k < X < 80 + k) = .08$, then
    $\displaystyle P\left({\frac{-k}{10} < Z < \frac{k}{10}}\right) = P\left({|Z| < \frac{k}{10}}\right) = 0.08$

    this implies that $\displaystyle P\left({Z < \frac{k}{10}}\right) = 0.08 + \left({0.5 - \frac{0.08}{2}}\right) = 0.54$
    which implies that $\displaystyle \frac{k}{10} = .1004 \implies k=1.004$

    indeed, you might be right..
    try checking this.. Z table - Normal Distribution
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Standard normal distribution
    Posted in the Statistics Forum
    Replies: 3
    Last Post: Jun 20th 2010, 05:56 PM
  2. Standard Normal Distribution
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Jan 21st 2009, 09:44 AM
  3. standard normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Sep 24th 2008, 12:46 AM
  4. standard normal distribution
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Jul 26th 2007, 11:57 AM
  5. standard normal question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Oct 4th 2006, 12:19 AM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum