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Statistics Problem

  • 27-04-2013 02:46PM
    #1
    paul4green
    Registered Users, Registered Users 2 Posts: 92 ✭✭


    " A machine producing vitamin E capsules operates so that the actual amount of vitamin E in the capsule is normally distributed with a mean of 10mg and a standard deviation of 0.05mg"

    Q (iii) If 5 such capsules are selected randomly, what is the probability that their average vitamin E content is at least 9.975mg??

    In simple terms is much appreciated !! lol


Comments

  • #2
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    This is a question about the "sampling distribution of the mean".

    When you take random samples of a certain size from a normal distribution, the means of these samples will have their own distribution, which will also be normal. The mean of this distribution of sample means is the same as the population mean. Its standard deviation is sigma/sqrt(n), where sigma is the standard deviation of the population and n is the size of the samples (in this case, 5).

    So, have a go. If you get stuck, post back with what you've tried.


  • #3
    paul4green
    Registered Users, Registered Users 2 Posts: 92 ✭✭paul4green


    So it would be 0.05/sqrt(5) = 0.0223?? is that right? :)


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