CA Foundation · Quantitative Aptitude · Theoretical Distributions
The mean of a binomial distribution is 12 and its variance is 3. What is the number of trials n?
Dividing variance by mean gives q = 3/12 = 0.25, so p = 0.75. Then n = mean/p = 12/0.75 = 16. Check: npq = 16 × 0.75 × 0.25 = 3, which matches the given variance.
- A16Correct
- B24
- C12
- D48
Explanation
np = 12 and npq = 3, so q = 3/12 = 0.25 and p = 0.75. Then n = 12/0.75 = 16. Check: 16 × 0.75 × 0.25 = 3. The value 48 comes from wrongly using p = 0.25.
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