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Homework Help: Normal distribution question

  1. May 15, 2009 #1
    1. The problem statement, all variables and given/known data

    3 (a) A sample of 50 washed baking potatoes was selected at random from a large batch.
    The weights of the 50 potatoes were found to have a mean of 234 grams and a standard
    deviation of 25.1 grams.
    Construct a 95% confidence interval for the mean weight of potatoes in the batch.
    (4 marks)

    2. Relevant equations

    [itex] \bar{x} = \mu[/itex]

    [itex] s = \frac{\sigma}{\sqrt{n}}[/itex]

    [itex] z = \frac{x-\mu}{s}[/itex]

    3. The attempt at a solution

    The confidence interval 95% means p = 0.975

    [itex] z = \frac{x-\mu}{s}[/itex]

    [itex] \pm 1.96 = \frac{x-234}{\frac{25.1}{\sqrt{50}}}[/itex]

    [itex]\Rightarrow 227-241[/itex]

    Why is the standard deviation

    [itex]s = \frac{25.1}{\sqrt{50}}[/itex]

    and not just 25.1. The question states that the s.d. is 25.1!
  2. jcsd
  3. May 15, 2009 #2
    [itex]\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} [/itex] is approximately N(0,1) for large n (assuming that the original distribtuion is not skewed)
  4. May 15, 2009 #3


    Staff: Mentor

    There are two things going on here. On the one hand there are the population standard deviation ([itex]\sigma[/itex] and sample standard deviation s. On the other is the standard deviation of the mean, which is defined as:
    [tex]\sigma_{mean} = \frac{\sigma}{\sqrt{n}}[/tex]

    The wikipedia article here--http://en.wikipedia.org/wiki/Standard_deviation--talks [Broken] about the st. dev. of the mean in the section titled Relationship between standard deviation and mean.
    Last edited by a moderator: May 4, 2017
  5. May 15, 2009 #4
    That's what's confusing, the standard deviation of the mean is the same as the standard deviation of the sample divided by root n?
    Last edited by a moderator: May 4, 2017
  6. May 15, 2009 #5
    It's approximately the same.
  7. May 16, 2009 #6
    s =SIGMA/SQRT(N)

  8. May 16, 2009 #7
    The standard deviation of the sample mean is sometimes called the standard error.
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