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Math Help - the normal curve

  1. #1
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    the normal curve

    I got halfway through this problem but am stumped on D and E.
    The amount of active ingredient in a certain type of cold remedy tablet has mean 400.0 milligrams and standard deviation 4.5 milligrams. If a sample of 72 tablets is randomly selected, what is the probability that the mean amount of active ingredients in this sample is more than 401 milligrams?

    A) Let x denote the amount of active ingredient in the cold remedy tablets. What’s known about the shape of the distribution of X?
    It is a bell curve
    B) Let X denote the mean amount of active ingredient in a sample of 72 of these cold remedy tablets. What is known about the shape of X-bar and why?
    i. It is a normal distribution because the sample size, n, is greater than 30.
    C) What is the mean of X-bar?
    Mean of x-bar equals 400.0 because M of x-bar equals the M of x
    D) What is the standard deviation of X-bar?
    E) Solve the problem
    Last edited by statisticsStudent; May 19th 2010 at 11:41 AM.
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  2. #2
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    D) If the population has standard deviation \sigma, then the standard deviation of the mean of a sample of size n is \sigma / \sqrt{n}.
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  3. #3
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    Thanks, awkward.

    I calculated the standard deviation as standard deviation of x-bar = standard deviation of x divided by the square root of n, or 4.5 divided by the square root of 72, and got .530

    I also calculated the Probability by converting the 401 milligrams to a z-score (1.89) and the calculating the normalcdf on my calculator (1.89, 1000) to come up with .0293, or probability of about 3 %

    Does this sound accurate?
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  4. #4
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    Correct!
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