Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2019 › Q11
0 marksStatistics › Sampling distributions and limit theorems › The central limit theorem and probability inequalitiesModerateabout 2 min

DSE 2019 Question 11: Sampling distributions and limit theorems

The random variable XXX denotes the number of successes in a sequence of independent trials, each with probability ppp of success. Let Xˉ\bar XXˉ denote the mean number of successes. We know that Xˉ\bar XXˉ:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

The random variable X denotes the number of successes in a sequence of independent trials, each with probability p of success. Let X̄ denote the mean number of successes. We know that X̄: (A) approximates a Normal distribution with mean p (B) has a Binomial distribution with mean p (C) None of the above (D) has a Normal distribution with mean p

Also written as: The random variable X denotes the number of successes in a sequence of independent trials, each with probability p of success. Let X_bar denote the mean number of successes. We know that X_bar:

Sampling distributions and limit theorems has come up 25 times in 7 exams since 2007.

What this question tests

This question is on The central limit theorem and probability inequalities, part of Sampling distributions and limit theorems in Statistics.

Why sample means are approximately normal, and bounds that hold for any distribution.

TestStop has 5 past-paper questions on this subtopic.

Practise Sampling distributions and limit theoremsMore on The central limit theorem and probability inequalities

Similar questions from other papers

  • GATE 2026 · Q47Suppose that X₁,X₂,X₃ and X₄ are independent random variables with common distribution N(4,12). Observations x₁=6,x₂=3,x₃=1, and x₄=10 correspond to X₁,X₂,X₃ and X₄…
  • CUET-PG 2025 · Q23In statistics, standard error measures the
  • UGC-NET 2025 · Q55Match List-I with List-II (properties of the Chi-square distribution): A. beta_1 (skewness measure) for Chi-square B. Skewness for Chi-square C. Mode for Chi-square D.…
  • IIT JAM 2024 · Q36Let X₁, X₂, …, Xₙ (n > 1) be a random sample from a distribution with mean μ and non-zero variance σ². Which of the following is/are CORRECT?
  • CUET-PG 2023 Shift 1 · Q99If you draw a random sample of size 25 from a population whose standard deviation is 10, what will be the standard error of sample mean?

Question from the DSE 2019 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.