CA Foundation · Quantitative Aptitude · Theoretical Distributions
A binomial variable X has n = 8 and p = 0.5. Which statement about its distribution is correct, and what is P(X = 4)?
With p = 0.5 the binomial distribution is symmetric about its mean. P(X = 4) = 8C4 × (1/2)^8 = 70/256, since 8C4 = 70. Options with skewness or the coefficient 56 are wrong.
- ASymmetric; P(X=4) = 70/256Correct
- BSymmetric; P(X=4) = 56/256
- CPositively skewed; P(X=4) = 70/256
- DNegatively skewed; P(X=4) = 56/256
Explanation
When p = 0.5 the binomial distribution is symmetric. P(X=4) = 8C4 × (0.5)^8 = 70/256. The value 56/256 is 8C3 or 8C5 over 256, which is the wrong coefficient for X = 4.
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