A binomial distribution achieves symmetry when:______________?
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Answer: D. Both (b) & (c) but not (a)
Explanation
A binomial distribution becomes perfectly symmetrical when the probability of success equals one half. When p equals 0.5, the probability of failure q also equals 0.5, satisfying the symmetry condition. Therefore, both statement b and statement c correctly describe the identical mathematical condition for symmetry. The binomial distribution formula calculates probabilities based on trials, success probability p, and failure q. Asymmetrical distributions occur when success and failure probabilities diverge significantly from each other. The binomial curve approaches a normal bell shape as the number of trials increases substantially.
Coin tossing experiments perfectly illustrate symmetrical binomial distributions because heads and tails are balanced. Binomial symmetry simplifies hypothesis testing because tail probabilities are identical on both sides. Understanding distribution shape helps statisticians choose appropriate approximation methods for large sample sizes. Option A is wrong because p greater than q creates a negatively skewed distribution curve. Option B is correct but incomplete because it ignores the equivalent phrasing found in option c. Option C is correct but incomplete because option b states the exact numerical equivalent.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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