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Is the following statement true? Justify your answer to get credit: “If X1, · · · , Xn are independently distributed, then for large enough n, the central limit theorem says that the sample mean Xn has a normal distribution.”

Respuesta :

Using the Central Limit Theorem, it is found that the statement is true, as for sample sizes of 30 or more, the sampling distribution of sample means is normal.

What does the Central Limit Theorem state?

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

Hence, the statement is true, as for sample sizes of 30 or more, the sampling distribution of sample means is normal, no matter the underlying distribution of the variable.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

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