Match List-I with List-II
| List-I | List-II | ||
| (A) | Mean of a binomial distribution with \(n = 20\), \(p = 0.3\) | (I) | 10 |
| (B) | Variance of a binomial distribution with \(n = 50\), \(p = 0.1\) | (II) | 3 |
| (C) | Standard deviation of a binomial distribution with \(n = 36\), \(p = \displaystyle\frac{1}{2}\) | (III) | 6 |
| (D) | Number of trials of a binomial distribution with mean 5 and variance 2.5 | (IV) | 4.5 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
For a binomial distribution, mean = np, variance = npq and standard deviation = \(\sqrt{npq}\), where q = 1 − p.
(A) Mean with n = 20, p = 0.3
This matches (III) 6.
\(np = 20 \times 0.3 = 6\)
(B) Variance with n = 50, p = 0.1
This matches (IV) 4.5.
\(npq = 50 \times 0.1 \times 0.9 = 4.5\)
(C) Standard deviation with n = 36, p = \(\frac{1}{2}\)
This matches (II) 3.
\( \displaystyle npq = 36 \times \frac{1}{2} \times \frac{1}{2} = 9 \)
\(\sqrt{9} = 3\)
(D) Number of trials with mean 5 and variance 2.5
This matches (I) 10.
\( \displaystyle q = \frac{2.5}{5} = 0.5,\quad p = 0.5 \)
\( \displaystyle n = \frac{5}{0.5} = 10 \)