The standard deviations of $x_i (i=1, 2, \ldots, 10)$ and $y_i (i=1, 2, \ldots, 10)$ are $a$ and $b$ respectively. $\bar{x}$ and $\bar{y}$ are the means of these two sets of observations. If $z_i = (x_i - \bar{x})(y_i - \bar{y})$ and $\sum_{i=1}^{10} z_i = c$,then the standard deviation of the observations $(x_i - y_i)$ for $i=1, 2, \ldots, 10$ is:

• A
  $\sqrt{a^2 + b^2 + \frac{c}{5}}$
• B
  $\sqrt{a^2 + b^2 - \frac{c}{5}}$
• C
  $\sqrt{a^2 + b^2 - \frac{c^2}{5}}$
• D
  $\sqrt{a^2 + b^2 + \frac{c^2}{5}}$