\begin{enumerate}[label=(\roman*)]
\item The manager of a company that employs 250 travelling sales representatives wishes to carry out a detailed analysis of the expenses claimed by the representatives. He has an alphabetical (by surname) list of the representatives. He chooses a sample of representatives by selecting the 10th, 20th, 30th and so on. Name the type of sampling the manager is attempting to use. Describe a weakness in his method of using it, and explain how he might overcome this weakness. [3]
\end{enumerate}

The representatives each use their own cars to drive to meetings with customers. The total distance, in miles, travelled by a representative in a month is Normally distributed with mean 2018 and standard deviation 96.

\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the probability that, in a randomly chosen month, a randomly chosen representative travels more than 2100 miles. [3]

\item Find the probability that, in a randomly chosen 3-month period, a randomly chosen representative travels less than 6000 miles. What assumption is needed here? Give a reason why it may not be realistic. [5]

\item Each month every representative submits a claim for travelling expenses plus commission. Travelling expenses are paid at the rate of 45 pence per mile. The commission is 10\% of the value of sales in that month. The value, in £, of the monthly sales has the distribution N(21200, 1100²). Find the probability that a randomly chosen claim lies between £3000 and £3300. [7]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI S3 2010 Q1 [18]}}