A particular population has a mean of 100 and a standard deviation of 20. If rep
ID: 3152025 • Letter: A
Question
A particular population has a mean of 100 and a standard deviation of 20. If repeated random samples of size n are taken and the sample means are found, according to the Central Limit Theorem, as n increases,
the distribution of x-bar has mean 100 and standard deviation 20.
the distribution of x-bar approaches the population distribution.
the distribution of x-bar approaches a normal distribution.
the distribution of x-bar cannot be determined because the samples were random.
the distribution of x-bar has mean 100 and standard deviation 20.
the distribution of x-bar approaches the population distribution.
the distribution of x-bar approaches a normal distribution.
the distribution of x-bar cannot be determined because the samples were random.
Explanation / Answer
A particular population has a mean of 100 and a standard deviation of 20. If repeated random samples of size n are taken and the sample means are found, according to the Central Limit Theorem, as n increases,
the distribution of x-bar has mean 100 and standard deviation 20.
the distribution of x-bar approaches the population distribution.
the distribution of x-bar approaches a normal distribution.
the distribution of x-bar cannot be determined because the samples were random.
The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough.
the distribution of x-bar has mean 100 and standard deviation 20.
the distribution of x-bar approaches the population distribution.
the distribution of x-bar approaches a normal distribution.
the distribution of x-bar cannot be determined because the samples were random.
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