3 At Heathwick airport each passenger’s luggage is weighed before being loaded into the hold of the aeroplane. Each weight is displayed digitally in kg to 1 decimal place. Some examples are given in Fig. 3.
\begin{table}[h]
| Weight (kg) |
| 17.2 |
| 19.9 |
| 22.3 |
| 20.1 |
| 21.5 |
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{table}
On each flight, the total weight of luggage is calculated to ensure compliance with health and safety regulations.
Winston models this situation by assuming that the displayed weights are rounded to 1 decimal place, and that the total weight of luggage is calculated using the displayed values.
On a flight to Athens, there are 154 items of passengers’ luggage.
- Determine the maximum possible error, according to Winston's model, when the total weight of luggage is calculated for the flight to Athens.
Piotre models this situation by assuming that the displayed weights are chopped to 1 decimal place, and that the total weight of luggage is calculated using the displayed values.
- Determine the maximum possible error, according to Piotre's model, when the total weight of luggage is calculated for the flight to Athens.
A health and safety inspector notes that the total of the displayed weights is 3080.2 kg . However, when the luggage is all weighed together in the loading bay, the total weight is found to be 3089.44 kg .
- Determine whether Winston's model or Piotre's model is a better fit for the data.