CUET · MATHS · PYQ PAPER 2025

Which of the following is not correct about the Central Limit Theorem?

A The sampling distribution of the sample mean approaches a bell-shaped curve as the sample size gets larger.
B A sample size of 30 or more is considered to be sufficient to hold the Central Limit Theorem.
C As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.
D The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.

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Answer & Solution

Correct Answer

(D) The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.

Step-by-step Solution

Detailed explanation

The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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List-I	List-II
(A) \(P(A \cap B)\)	(I) 0.5
(B) \(P(A \mid B)\)	(II) 0.8
(C) \(P(A \cup B)\)	(III) 0.25
(D) \(P\left(A^{\prime}\right)\)	(IV) 0.1

List - I	List - II
(A) P(X = 0)	(I) \(\frac{1}{216}\)
(B) P(X = 1)	(II) \(\frac{15}{216}\)
(C) P(X = 2)	(III) \(\frac{75}{216}\)
(D) P(X = 3)	(IV) \(\frac{125}{216}\)