Match List - I with List - II. List I — n = number of trials, p = probability…
2024
Match List - I with List - II.
List I — n = number of trials, p = probability of success | List II — Variance of Binomial Distribution |
|---|---|
A. n = 7, p = 0.3 | I. 1.44 |
B. n = 5, p = 0.4 | II. 2.00 |
C. n = 8, p = 0.5 | III. 1.20 |
D. n = 6, p = 0.6 | IV. 1.47 |
Choose the correct answer from the options given below :
Answer: D. A-IV, B-III, C-II, D-I — ConceptFor a binomial random variable X with parameters n and p, the variance is Var(X) = npq, where q = 1 − p. The factor p(1 − p) is the variance of one…
- A.
A-I, B-II, C-III, D-IV
- B.
A-II, B-III, C-IV, D-I
- C.
A-III, B-IV, C-I, D-II
- D.
A-IV, B-III, C-II, D-I
Show answer & explanation
Correct answer: D
Concept
For a binomial random variable X with parameters n and p, the variance is Var(X) = npq, where q = 1 − p. The factor p(1 − p) is the variance of one Bernoulli trial, and multiplying it by n combines the contributions of n independent trials.
Application
For A, q = 1 − 0.3 = 0.7, so the variance is 7 × 0.3 × 0.7 = 1.47. Therefore, A maps to IV.
For B, q = 1 − 0.4 = 0.6, so the variance is 5 × 0.4 × 0.6 = 1.20. Therefore, B maps to III.
For C, q = 1 − 0.5 = 0.5, so the variance is 8 × 0.5 × 0.5 = 2.00. Therefore, C maps to II.
For D, q = 1 − 0.6 = 0.4, so the variance is 6 × 0.6 × 0.4 = 1.44. Therefore, D maps to I.
Cross-check
The four computations use each listed variance exactly once: A–IV, B–III, C–II, and D–I. Thus the accepted mapping is A-IV, B-III, C-II, D-I.