CUET · MATHS · PYQ PAPER 2025

If \(X\) is a normal variate with mean 12 and standard deviation 4, then \(P(X \geq 20)\) is :
[Given that \(P(0 \leq Z \leq 2)=0.4772\) ]

A 0.9772
B 0.0228
C 0.00135
D 0.7563

Verified Solution

Answer & Solution

Correct Answer

(B) 0.0228

Step-by-step Solution

Detailed explanation

\(Z = \frac{X - \mu}{\sigma}\) \(Z = \frac{20 - 12}{4} = 2\) \(P(X \geq 20) = P(Z \geq 2)\) \(P(Z \geq 2) = 0.5 - P(0 \leq Z \leq 2)\) \(P(Z \geq 2) = 0.5 - 0.4772 = 0.0228\)

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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Match List I with List - II.

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(B) LED	(II) operates under reverse bias
(C) Solar cell	(III) operates under reverse bias in break down region
(D) Photo diode	(IV) no biasing is applied

Choose the correct answer from the options given below :

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If \(X\) is a normal variate with mean 12 and standard deviation 4, then \(P(X \geq 20)\) is :[Given that \(P(0 \leq Z \leq 2)=0.4772\) ]

Step-by-step Solution

If \(X\) is a normal variate with mean 12 and standard deviation 4, then \(P(X \geq 20)\) is :
[Given that \(P(0 \leq Z \leq 2)=0.4772\) ]