Question 438120: If x has a normal distribution with a mean 15 and standard deviation 3, describe
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the distribution of x values for sample size n, where n=4, n=16, and n =100. How
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do the x distributions compare for the various sample sizes?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If x has a normal distribution with a mean 15 and standard deviation 3, describe the distribution of x values for sample size n, where n=4, n=16, and n =100. How do the x distributions compare for the various sample sizes?
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The mean of the sample means of any size = the mean of the population.
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The std of the sample means for samples of size n = s/sqrt(n) where
s is the std of the population.
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mean for all your distributions is 15
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std for samples of size 4 is 3/sqrt(4) = 3/2
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std of samples of size 16 is 3/sqrt(16) = 3/4
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std of samples of size 100 = 3/sqrt(100) = 3/10
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Notice: As the samples size gets larger the spread of the
distribution gets smaller, or tighter.
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Cheers,
Stan H.
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