Match List - I with List - II.

Choose the correct answer from the options given below:

(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

The correct answer is Option (2) - (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

$\text{(A)}\; n=10,\; q=0.25 \Rightarrow p=0.75$

$\text{Mean} = np = 10 \times 0.75 = 7.5 \Rightarrow \text{matches (II)}$

$\text{(B)}\; \text{Mean}=6,\; \text{Variance}=3$

$np=6,\; npq=3 \Rightarrow q=\frac{3}{6}=\frac{1}{2} \Rightarrow p=\frac{1}{2} \Rightarrow \text{matches (IV)}$

$\text{(C)}\; p=\frac{1}{4},\; \sigma=3 \Rightarrow npq=9$

$n \cdot \frac{1}{4}\cdot \frac{3}{4} = 9 \Rightarrow \frac{3n}{16}=9 \Rightarrow n=48$

$\text{Mean}=np=48 \cdot \frac{1}{4}=12 \Rightarrow \text{matches (I)}$

$\text{(D)}\; \text{Mean}=4,\; \text{Variance}=3$

$np=4,\; npq=3 \Rightarrow q=\frac{3}{4},\; p=\frac{1}{4}$

$n=\frac{4}{1/4}=16 \Rightarrow \text{matches (III)}$

A–II,\; B–IV,\; C–I,\; D–III