1. Given data

   • First sample: $n_1=100,\quad \bar x_1=15,\quad \sigma_1=3$
   • Whole group: $N=250,\quad \bar x=15.6,\quad \sigma=\sqrt{13.44}$
   • Therefore second sample size: $n_2=250-100=150$

2. Find the mean of the second sample

   Using combined mean: $\bar x=\frac{n_1\bar x_1+n_2\bar x_2}{n_1+n_2}$

   Substitute values: $15.6=\frac{100\cdot 15+150\cdot \bar x_2}{250}$

   $15.6\cdot 250=1500+150\bar x_2$

   $3900=1500+150\bar x_2$

   $150\bar x_2=2400$

   $\bar x_2=16$

3. Use combined variance formula

   For combined variance: $\sigma^2=\frac{n_1\left(\sigma_1^2+(\bar x_1-\bar x)^2\right)+n_2\left(\sigma_2^2+(\bar x_2-\bar x)^2\right)}{n_1+n_2}$

   Here, $\sigma^2=13.44$ $\sigma_1^2=3^2=9$ $\bar x_1-\bar x=15-15.6=-0.6\Rightarrow (\bar x_1-\bar x)^2=0.36$ $\bar x_2-\bar x=16-15.6=0.4\Rightarrow (\bar x_2-\bar x)^2=0.16$

   So, $13.44=\frac{100(9+0.36)+150(\sigma_2^2+0.16)}{250}$

4. Simplify

   $13.44=\frac{100(9.36)+150(\sigma_2^2+0.16)}{250}$

   $13.44=\frac{936+150\sigma_2^2+24}{250}$

   $13.44=\frac{960+150\sigma_2^2}{250}$

   Multiply by 250: $3360=960+150\sigma_2^2$

   $150\sigma_2^2=2400$

   $\sigma_2^2=16$

   $\sigma_2=4$

5. Check options

   • A: 8 ❌
   • B: 6 ❌
   • C: 4 ✅
   • D: 5 ❌

Therefore, the standard deviation of the second sample is: $\boxed{4}$