Results 1 to 5 of 5

Math Help - Normal distribution question involving samples

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    15

    Normal distribution question involving samples

    Q: The mass of coffee in a randomly chosen jar sold by a certain company may be taken to have a normal distribution with mean 203g and standard deviation 2.5g. The random variable C denotes the mean mass (in grams) of coffee jar per in a random sample of 20 jars, find the value of a such that P(|C - 203| < a) = 0.95.

    How to solve this question?

    Thanks in advance!!!
    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 Cathelyn13 View Post
    Q: The mass of coffee in a randomly chosen jar sold by a certain company may be taken to have a normal distribution with mean 203g and standard deviation 2.5g. The random variable C denotes the mean mass (in grams) of coffee jar per in a random sample of 20 jars, find the value of a such that P(|C - 203| < a) = 0.95.

    How to solve this question?

    Thanks in advance!!!
    You should realise that C ~ Normal \left( \mu = 203, ~ \sigma = \frac{2.5}{\sqrt{20}}\right).

    Therefore X = C - 203 ~ Normal \left( \mu = 0, ~ \sigma = \frac{2.5}{\sqrt{20}}\right).

    Now note that \Pr(|X| < a) = \Pr(-a < X < a) = 1 - 2\Pr (X > a) by symmetry.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2009
    Posts
    15
    I see. But why the standard deviation has to be divided by the root of the sample size? Is there any formula to the finding the sample mean and sample standard deviation from the population mean and standard deviation?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Cathelyn13 View Post
    I see. But why the standard deviation has to be divided by the root of the sample size? Is there any formula to the finding the sample mean and sample standard deviation from the population mean and standard deviation?
    Have you covered the sampling distribution of the mean in class? The formula I used will be in your class notes or textbook.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2009
    Posts
    15
    I think so . Are you referring to: If X ~ N ( μ, δ ) then X bar ~ N (μ, δ /n)? Using this I can get the answer now. Thanks!!! =)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: January 24th 2011, 05:10 PM
  2. Maximization question involving normal distribution.
    Posted in the Business Math Forum
    Replies: 5
    Last Post: August 11th 2010, 10:14 AM
  3. Normal distribution question
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 9th 2009, 07:13 PM
  4. normal distribution question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 13th 2008, 04:38 AM
  5. greatest distribution of samples
    Posted in the Statistics Forum
    Replies: 3
    Last Post: June 22nd 2006, 05:44 AM

Search Tags


/mathhelpforum @mathhelpforum