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Even though the original random variable is not normally distributed the sample size is over 30 by the central limit theorem the sample mean will be normally distributed The mean of the sample mean is mu mathrm overline x mu 17 4 years
The central limit theorem in statistics states that given a sufficiently large sample size the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable s distribution in the population Unpacking the meaning from that complex definition can be difficult
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Central Limit Theorem
Central Limit Theorem
The sample size n is equal to 75 Because the individual stress scores follow a uniform distribution X U 1 5 where a 1 and b 5 see Continuous Random Variables for an explanation of a uniform distribution X a b 2 1 5 2 3 7 3 X b a 2 12 5 1 2 12 1 15 7 4
The Central Limit Theorem therefore tells us that the sample mean bar X is approximately normally distributed with mean mu bar X mu 3 and variance sigma 2 bar X dfrac sigma 2 n dfrac 6 n Again we ll follow a strategy similar to that in the above example namely Specify the sample size n
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Sampling Distributions And The Central Limit Theorem YouTube
Sampling Distributions And The Central Limit Theorem YouTube
12 years ago You are correct the deviation go to 0 as the sample size increases because you would get the same result each time because you are sampling the entire population
In probability theory the central limit theorem CLT states that under appropriate conditions the distribution of a normalized version of the sample mean converges to a standard normal distribution This holds even if the original variables themselves are not normally distributed
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https://statisticsbyjim.com/basics/central-
The central limit theorem in statistics states that given a sufficiently large sample size the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable s distribution in the population Unpacking the meaning from that complex definition can be difficult
https://www.statology.org/central-limit-theorem
If the population distribution is symmetric sometimes a sample size as small as 15 is sufficient If the population distribution is skewed generally a sample size of at least 30 is needed If the population distribution is extremely skewed then a sample size of 40 or higher may be necessary
The central limit theorem in statistics states that given a sufficiently large sample size the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable s distribution in the population Unpacking the meaning from that complex definition can be difficult
If the population distribution is symmetric sometimes a sample size as small as 15 is sufficient If the population distribution is skewed generally a sample size of at least 30 is needed If the population distribution is extremely skewed then a sample size of 40 or higher may be necessary
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