CA Foundation · Quantitative Aptitude · Theoretical Distributions
The mean of a binomial distribution is 9 and its standard deviation is 1.5. What is the value of p?
The variance is 1.5 squared, which is 2.25. Dividing variance by the mean 9 gives q = 0.25, so p = 1 − 0.25 = 0.75. This gives n = 12, and 12 × 0.75 × 0.25 = 2.25, confirming it. The 0.25 is q.
- A0.75Correct
- B0.25
- C0.36
- D0.80
Explanation
Variance = 1.5² = 2.25 = npq. Then q = 2.25/9 = 0.25, so p = 0.75. Check: n = 9/0.75 = 12 and 12 × 0.75 × 0.25 = 2.25. Option 0.25 is q, not p.
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