The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?

Let the original observations be $x_1, x_2, \dots, x_{100}$.

The standard deviation of these observations is $\sigma_x = 10$.

The new observations are given by $y_i = \dfrac{x_i + 5}{20} = \dfrac{1}{20}x_i + \dfrac{1}{4}$.

If a new variable is defined as $y_i = ax_i + b$, its standard deviation is given by $\sigma_y = |a|\sigma_x$.

Substituting $a = \dfrac{1}{20}$ and $\sigma_x = 10$:

$\sigma_y = \left| \dfrac{1}{20} \right| \times 10 = 0.5$

The new standard deviation is $0.5$.

Answer: $0.5$