A random variable X is 1 with probability p and 5 with probability 1 - p…

Step 1. Find $p$. $5 - 4p = 2$, so $p = 0.75$.

Step 2. The variance. $(1 - 2)^2 \times 0.75 + (5 - 2)^2 \times 0.25 = 0.75 + 2.25 = 3$.

Step 3. The standard deviation. $\sqrt{3} \approx 1.732$.

Step 4. Doubled. The new values are $2$ and $10$. Every distance from the new mean, $4$, is twice as long, so $\sigma = 2 \times 1.732 \approx 3.464$.