5 The Globe Express agency organises trips to the theatre. The cost, $\pounds X$, of these trips can be modelled by the following probability distribution:

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 40 & 45 & 55 & 74 \\
\hline
$\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )$ & 0.30 & 0.24 & 0.36 & 0.10 \\
\hline
\end{tabular}
\end{center}

(a) Calculate the mean and standard deviation of $X$.\\
(b) For special celebrity charity performances, Globe Express increases the cost of the trips to $\pounds Y$, where

$$Y = 10 X + 250$$

Determine the mean and standard deviation of $Y$.

\hfill \mbox{\textit{AQA S2  Q5}}