Consider four different Binomial distributions each with number of trials, n =…
2026
Consider four different Binomial distributions each with number of trials, n = 64 and probability of success, p as given in A-D below. Compute the variance for each Binomial distribution and arrange in ascending order.
A. p = 0.01 B. p = 0.3 C. p = 0.5 D. p = 0.9
- A.
A, D, B, C
- B.
B, C, A, D
- C.
D, A, C, B
- D.
C, B, D, A
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Correct answer: A
The variance of a Binomial distribution is calculated using the formula Var = n * p * (1 - p). Since n = 64 is constant, we compare the values of p * (1 - p).
For A (p = 0.01): Var = 64 * 0.01 * 0.99 = 0.6336. For B (p = 0.3): Var = 64 * 0.3 * 0.7 = 13.44. For C (p = 0.5): Var = 64 * 0.5 * 0.5 = 16. For D (p = 0.9): Var = 64 * 0.9 * 0.1 = 5.76.
Arranging the variances in ascending order gives A < D < B < C.