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MMLU-Pro / 8668 / Which of the following is the central limit theorem?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Which of the following is the central limit theorem?

category

math

options

  1. The central limit theorem states that the mean of a large number of independent and identically distributed random variables, each with finite mean and variance, will approximately follow a normal distribution.
  2. If the population is uniformly distributed, then as the sample size increases, the sampling distribution of the sample mean becomes closer to a normal distribution.
  3. No matter how the population is distributed, as the sample size increases, the standard deviation of the sample means becomes closer to the standard deviation of the population divided by the square root of the sample size.
  4. If the population is normally distributed, then as the sample size increases, the sampling distribution of the sample mean becomes closer to a normal distribution.
  5. The central limit theorem states that the median of a large number of independent and identically distributed random variables, each with finite mean and variance, will approximately follow a normal distribution.
  6. The central limit theorem refers to something else.
  7. The central limit theorem states that as the sample size increases, the median of the sample means becomes closer to the median of the population.
  8. No matter how the population is distributed, as the sample size increases, the mean of the sample means becomes closer to the mean of the population.
  9. Regardless of the distribution of the population, the variance of the sample means will converge to the variance of the population as the sample size increases.
  10. The central limit theorem states that the sum of a large number of independent and identically distributed random variables, each with finite mean and variance, will approximately follow a normal distribution, regardless of the shape of the original measurement distribution.

src

ori_mmlu-high_school_statistics

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Source and history

upstream_id / Original problem ID
8668
task_id
c7fcf1c4-0787-557b-ae4b-dd9a0e917b14
task_key
default--test--8668
task_revision_id
1
config / split
default / test

Official source

initial import