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Questions › DSE › DSE 2015 › Q50
2 marks, −0.666666666666667Statistics › Sampling distributions and limit theorems › The central limit theorem and probability inequalitiesHardabout 4 min

DSE 2015 Question 50: Sampling distributions and limit theorems

There exists a random variable XXX with mean μX\mu_XμX​ and variance σX2\sigma_X^2σX2​ for which P[μX−2σX≤X≤μX+2σX]=0.6P[\mu_X-2\sigma_X\le X\le\mu_X+2\sigma_X]=0.6P[μX​−2σX​≤X≤μX​+2σX​]=0.6. This statement is

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There exists a random variable X with mean μ_X and variance σ_X² for which P[μ_X-2σ_X≤ X≤μ_X+2σ_X]=0.6. This statement is (A) true for any distribution for appropriate μ_X,σ_X² (B) true only for the uniform distribution over an appropriate interval (C) true only for the normal distribution for appropriate μ_X,σ_X² (D) false

Also written as: There exists a random variable X with mean mu_X and variance sigma_X^2 for which P[mu_X-2sigma_X<= X<=mu_X+2sigma_X]=0.6. This statement is

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

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.