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The sampling distribution of the sample mean often has approximately a normal distribution. As the sample size increases, the sampling distribution of the sample mean has a more bell-shaped appearance. For relatively large sample sizes, the sampling distribution is bell shaped even if the population is highly discrete or highly skewed. This is known as the

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Answer:

For this case the best answer would be the "Central Limit theorem" or CLT since we are assuming that we have a large sample size (n>30) so then all the conditions are satisfied to assume a normal distribution for the sample mean [tex]\bar X[/tex]

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

Explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

Solution to the problem

For this case the best answer would be the "Central Limit theorem" or CLT since we are assuming that we have a large sample size (n>30) so then all the conditions are satisfied to assume a normal distribution for the sample mean [tex]\bar X[/tex]

luisvaschetto

When the sampling distribution is bell-shaped even if the population is highly discrete or highly skewed, it is known as the central limit theorem.

  • The central limit theorem indicates that the statistical distribution of sample means resembles normal distributions when the sample becomes larger.

  • The central limit theorem is independent of the distribution in the population.

  • A number equal to or higher than 30 is sufficient to apply the central limit theorem.

In conclusion, when the sampling distribution is bell-shaped even if the population is highly discrete or highly skewed, it is known as the central limit theorem.

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