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AP Statistics The Central Limit Theorem — practice questions

Explore 18 free The Central Limit Theorem questions in AP Statistics Statistics. Open each question or exercise to read its content, reference answers and available explanation.

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The Central Limit Theorem questions and exercises with answers

Showing questions 1–18 of 18.

As sample sizes increase, the distribution of sample means more closely follows the:Read the answer and worked solution →The law of large numbers says that as samples get larger, the sample mean gets:Read the answer and worked solution →The standard deviation of the sampling distribution is the population standard deviation divided by:Read the answer and worked solution →The standard deviation of the distribution of sample means is usually called the:Read the answer and worked solution →If the original population is far from normal, the central limit theorem needs:Read the answer and worked solution →Quadrupling the sample size changes the standard error by a factor of:Read the answer and worked solution →The central limit theorem applies to sample means taken from:Read the answer and worked solution →Doubling the sample size makes the sampling distribution of the mean:Read the answer and worked solution →The mean of the sampling distribution of sample means equals:Read the answer and worked solution →Standard deviation is related to variance as its:Read the answer and worked solution →Recognising a central limit theorem problem means spotting a question about:Read the answer and worked solution →A population that is already close to normal needs which sample size for the theorem to apply well?Read the answer and worked solution →Comparing the law of large numbers with the central limit theorem, the law of large numbers is about the:Read the answer and worked solution →The standard error appears in calculator routines as a parameter alongside:Read the answer and worked solution →Match each sampling ideaRead the answer and worked solution →True or false: sampling distributionsRead the answer and worked solution →Which has the smaller standard error?Read the answer and worked solution →Complete the sampling rulesRead the answer and worked solution →

Worked practice questions

As sample sizes increase, the distribution of sample means more closely follows the:

  1. Normal distribution
  2. Uniform distribution
  3. Binomial distribution
  4. Original distribution
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Correct answer: A. Normal distribution

1. The central limit theorem is a statement about what happens to averages. 2. As sample sizes increase, the distribution of means more closely follows the normal distribution. 3. That is true whatever shape the original population had. 4. It is why normal-based methods work so widely in practice. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_

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The law of large numbers says that as samples get larger, the sample mean gets:

  1. Larger without any limit
  2. Closer to the population mean
  3. Further from the population mean
  4. Closer to exactly zero
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Correct answer: B. Closer to the population mean

1. Averaging more observations makes an estimate steadier. 2. The law of large numbers says that if you take samples of larger and larger size from any population then the mean of the sample tends to get closer and closer to the population mean. 3. So a big sample gives a more trustworthy estimate of the centre. 4. The estimate settles on the true mean rather than on zero. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_

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The standard deviation of the sampling distribution is the population standard deviation divided by:

  1. The square root of n
  2. The value of n itself
  3. The square of n
  4. Twice the value of n
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Correct answer: A. The square root of n

1. Averages vary less than individual observations do. 2. Standard deviation is the square root of variance. 3. The standard deviation of the sampling distribution is the standard deviation of the original distribution divided by the square root of n. 4. That shrinking spread is exactly why bigger samples give tighter estimates. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_

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