To explain:Whether the given statement is correct or not

lwfrgin 2021-01-31 Answered
To explain:Whether the given statement is correct or not
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Expert Answer

Faiza Fuller
Answered 2021-02-01 Author has 108 answers

Given information:
The given statement is,
"if x is the mean of a large (n > 30) simple random from a population with mean \mu and standard deviation σ , then x is approximately normal with σx=σn.
The central limit theorem is one of the important concepts of the large sample theory.
According to the central limit theorem, for a sufficiently large sample size, the sampling distributions of the mean tend to be normal distribution, irrespective of the distribution of the population.Generally, a sample size more than 30 is considered a large sample.
The sampling distribution of the sample mean bar x for the large samples follows normal distribution with mean and variance σ2n , where mu is the population mean, n is the sample size and σ2 is the population variance, that is,
xsimN(μ,σn)
xsimN(μ,σx)
Thus, the provided statement is true.

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