CUET · MATHS · PYQ PAPER 2025

If \(95 \%\) confidence interval for the population mean was reported to be 140 to 150 and \(\sigma=25\), then the size of the sample used in this study is:
[Given: \(Z_{0.025}=1.96\) ]

A 120
B 81
C 96
D 112

Verified Solution

Answer & Solution

Correct Answer

(C) 96

Step-by-step Solution

Detailed explanation

\( ME = \frac{150-140}{2} = 5 \) \( ME = Z_{\alpha/2} \frac{\sigma}{\sqrt{n}} \) \( 5 = 1.96 \frac{25}{\sqrt{n}} \) \( \sqrt{n} = \frac{1.96 \times 25}{5} = 9.8 \) \( n = (9.8)^2 = 96.04 \) \( n \approx 96 \)

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) Point of minima of \(f(x)=\|x+1\|\)	(I) 1
(B) Minimum value of \(f(x)=\|x\|\)	(II) -1
(C) Maximum value of \(f(x)=1-x^2\)	(III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\)	(IV) 0

If \(95 \%\) confidence interval for the population mean was reported to be 140 to 150 and \(\sigma=25\), then the size of the sample used in this study is:[Given: \(Z_{0.025}=1.96\) ]

Step-by-step Solution

If \(95 \%\) confidence interval for the population mean was reported to be 140 to 150 and \(\sigma=25\), then the size of the sample used in this study is:
[Given: \(Z_{0.025}=1.96\) ]