4 A ski-lift gondola can carry 4 people. The weight restriction sign in the gondola says "4 people - 325 kg ".
The table models the distribution of weights of people using the gondola.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Men | Women | Children |
| Weight \(( \mathrm { kg } )\) | 90 | 80 | 40 |
| Probability | \(\frac { 1 } { 2 }\) | \(\frac { 1 } { 3 }\) | \(\frac { 1 } { 6 }\) |
- Give an efficient rule for using 2-digit random numbers to simulate the weight of a person entering the gondola.
- Give a reason for using 2-digit rather than 1-digit random numbers in these circumstances.
- Using the random numbers given in your answer book, simulate the weights of four people entering the gondola, and hence give its simulated load.
- Using the random numbers given in your answer book, repeat your simulation 9 further times. Hence estimate the probability of the load of a fully-laden gondola exceeding 325 kg .
- What in reality might affect the pattern of loading of a gondola which is not modelled by your simulation?