3.8 is the mean of 5 positive numbers a, b, c, d and e.
The sum of their squares is 360. Each of the numbers is now multiplied by 2.
Find the new standard deviation. Answer ...

1. Find the original standard deviation from the mean and sum of squares.

For the original 5 numbers,
$\bar{x}=3.8,\quad n=5,\quad \sum x^2=360.$
$\text{standard deviation}=\sqrt{\frac{360}{5}-(3.8)^2}$
$=\sqrt{72-14.44}$
$=\sqrt{57.56}$

2. Apply the effect of multiplying all data values by 2.

When each number is multiplied by $2$, the standard deviation is also multiplied by $2$.
$\text{new standard deviation}=2\sqrt{57.56}$
$=16.96\ldots$