Results 1 to 2 of 2

Math Help - sample means...need help

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    25

    sample means...need help

    Distances between students' homes and school observe normal distribution with mean of 4.76 miles and standard deviation of 1.74 miles. Suppose all examples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

    Z=Mean-mean of sample means/ std of sample means, so i have

    Z=6.78-4.76/(1.74/sqrt[12])=4.02

    I know the next step is to look for a percentage in the table that corresponds to this zscore, but I can't find 4.02 in the table? Can someone talk me through what I *should* be looking for? step by step?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by peanutbutter View Post
    Distances between students' homes and school observe normal distribution with mean of 4.76 miles and standard deviation of 1.74 miles. Suppose all examples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

    Z=Mean-mean of sample means/ std of sample means, so i have

    Z=6.78-4.76/(1.74/sqrt[12])=4.02

    I know the next step is to look for a percentage in the table that corresponds to this zscore, but I can't find 4.02 in the table? Can someone talk me through what I *should* be looking for? step by step?
    The sample mean is a random variable and follows a normal distribution.

    In fact, if you let \bar{X} represent the random variable mean of the sample, then

    \bar{X} ~ Normal \left( \mu = 4.76, ~ \sigma = \frac{1.74}{\sqrt{12}} \approx 0.5\right).

    You first need to find \Pr \left(\bar{X} > 6.78\right):

    Z = \frac{6.78 - 4.76}{0.5} = 4.04.

    This z-value is really, really big (more than 4 standard deviations from the mean) so it's no surprise that you can't find it in your tables. \Pr(Z > 4.04) = 0, correct to four decimal places.


    Then you multiply the answer by 100 to convert into a percentage: 0%.
    Last edited by mr fantastic; July 3rd 2008 at 02:59 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Comparing means from SAME sample
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 1st 2010, 12:57 PM
  2. Two means in one sample
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 24th 2010, 12:44 AM
  3. Replies: 1
    Last Post: April 29th 2010, 02:51 AM
  4. Covariance of two sample means
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: June 20th 2009, 07:03 PM
  5. sampling distribution of sample means
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: December 31st 2007, 09:47 AM

Search Tags


/mathhelpforum @mathhelpforum