5 Still mineral water is supplied in 1.5-litre bottles. The actual volume, $X$ millilitres, in a bottle may be modelled by a normal distribution with mean $\mu = 1525$ and standard deviation $\sigma = 9.6$.
\begin{enumerate}[label=(\alph*)]
\item Determine the probability that the volume of water in a randomly selected bottle is:
\begin{enumerate}[label=(\roman*)]
\item less than 1540 ml ;
\item more than 1535 ml ;
\item between 1515 ml and 1540 ml ;
\item not 1500 ml .
\end{enumerate}\item The supplier requires that only 10 per cent of bottles should contain more than 1535 ml of water.

Assuming that there has been no change in the value of $\sigma$, calculate the reduction in the value of $\mu$ in order to satisfy this requirement. Give your answer to one decimal place.
\item Sparkling spring water is supplied in packs of six 0.5 -litre bottles. The actual volume in a bottle may be modelled by a normal distribution with mean 508.5 ml and standard deviation 3.5 ml .

Stating a necessary assumption, determine the probability that:
\begin{enumerate}[label=(\roman*)]
\item the volume of water in each of the 6 bottles from a randomly selected pack is more than 505 ml ;
\item the mean volume of water in the 6 bottles from a randomly selected pack is more than 505 ml .\\[0pt]
[7 marks]
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA S1 2016 Q5 [18]}}