6 Answer part (iv) of this question on the insert provided. There are two types of customer who use the shop at a service station. \(70 \%\) buy fuel, the other \(30 \%\) do not. There is only one till in operation.

1. Give an efficient rule for using one-digit random numbers to simulate the type of customer arriving at the service station. Table 6.1 shows the distribution of time taken at the till by customers who are buying fuel.

   Time taken (mins)	1	1.5	2	2.5
   Probability	\(\frac { 3 } { 10 }\)	\(\frac { 2 } { 5 }\)	\(\frac { 1 } { 5 }\)	\(\frac { 1 } { 10 }\)

   \section*{Table 6.1}
2. Specify an efficient rule for using one-digit random numbers to simulate the time taken at the till by customers purchasing fuel. Table 6.2 shows the distribution of time taken at the till by customers who are not buying fuel.

   Time taken (mins)	1	1.5	2	2.5	3
   Probability	\(\frac { 1 } { 7 }\)	\(\frac { 2 } { 7 }\)	\(\frac { 2 } { 7 }\)	\(\frac { 1 } { 7 }\)	\(\frac { 1 } { 7 }\)

   \section*{Table 6.2}
3. Specify an efficient rule for using two-digit random numbers to simulate the time taken at the till by customers not buying fuel. What is the advantage in using two-digit random numbers instead of one-digit random numbers in this part of the question? The table in the insert shows a partially completed simulation study of 10 customers arriving at the till.
4. Complete the table using the random numbers which are provided.
5. Calculate the mean total time spent queuing and paying.