STATISTICAL TECHNIQUES AND TOOLS
SAMPLING DISTRIBUTION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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Let X be a random variable that has a skewed distribution with mean µ = 10 and standard deviation = 10. Based on random samples of size 400, the sampling distribution of X is
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highly skewed with mean 10 and standard deviation 10
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highly skewed with mean 10 and standard deviation 5
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highly skewed with mean 10 and standard deviation 0.5
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approximately normal with mean 10 and standard deviation 10
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approximately normal with mean 10 and standard deviation 0.5
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Explanation:
Detailed explanation-1: -For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean ˉX= and standard deviation ˉX=/√n, where n is the sample size.
Detailed explanation-2: -1. The mean of the distribution of sample means is called the Expected Value of M and is always equal to the population mean . 3. The shape of the distribution of sample means tends to be normal.
Detailed explanation-3: -If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is (mu) and the population standard deviation is (sigma) then the mean of all sample means (x-bars) is population mean (mu).
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