CA Foundation · Quantitative Aptitude · Theoretical Distributions
A binomial distribution has mean 12 and variance 9. What are the values of n and p?
The correct values are n = 48 and p = 0.25. Dividing variance by mean gives q = 9/12 = 0.75, so p = 0.25, and n = mean divided by p = 12/0.25 = 48. Check: 48 x 0.25 x 0.75 equals 9.
- An = 48, p = 0.25
- Bn = 16, p = 0.75Correct
- Cn = 24, p = 0.5
- Dn = 12, p = 0.75
Explanation
Mean = np = 12 and variance = npq = 9. So q = 9/12 = 0.75 and p = 0.25. Then n = 12/0.25 = 48. Check: 48 x 0.25 x 0.75 = 9. Option n = 16, p = 0.75 is wrong because it takes p as 0.75 by mistaking q for p.
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