We know that \(\Sigma(x - 10) = 27\) and the mean number of emails is 11.5. The mean is given by \(\frac{\Sigma x}{n} = 11.5\).

First, express \(\Sigma x\) in terms of \(n\):

\(\Sigma x = 11.5n\).

We also have:

\(\Sigma(x - 10) = \Sigma x - 10n = 27\).

Substitute \(\Sigma x = 11.5n\) into the equation:

\(11.5n - 10n = 27\).

Simplify the equation:

\(1.5n = 27\).

Solving for \(n\):

\(n = \frac{27}{1.5} = 18\).