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If a Binomial distribution has mean 4 and variance 3, the value of p is
A0.5
B0.4
C0.75
D0.25
Answer & Solution
Correct answer: D. 0.25
1. Mean = np = 4; variance = npq = 3 ⇒ q = 3/4 ⇒ p = 1 − 3/4 = 1/4 = 0.25.
2. Cross-check: n = mean/p = 4/0.25 = 16 ⇒ npq = 16 × 0.25 × 0.75 = 3. ✓
3. All values reconcile.
4. Hence p = 0.25.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 8 "Probability Distributions", §8.1 ¶§8.1_
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