13 The table below is an extract from the Large Data Set.
| Propulsion Type | Region | Engine Size | Mass | \(\mathrm { CO } _ { 2 }\) | Particulate Emissions |
| 2 | London | 1896 | 1533 | 154 | 0.04 |
| 2 | North West | 1896 | 1423 | 146 | 0.029 |
| 2 | North West | 1896 | 1353 | 138 | 0.025 |
| 2 | South West | 1998 | 1547 | 159 | 0.026 |
| 2 | London | 1896 | 1388 | 138 | 0.025 |
| 2 | South West | 1896 | 1214 | 130 | 0.011 |
| 2 | South West | 1896 | 1480 | 146 | 0.029 |
| 2 | South West | 1896 | 1413 | 146 | 0.024 |
| 2 | South West | 2496 | 1695 | 192 | 0.034 |
| 2 | South West | 1422 | 1251 | 122 | 0.025 |
| 2 | South West | 1995 | 2075 | 175 | 0.034 |
| 2 | London | 1896 | 1285 | 140 | 0.036 |
| 2 | North West | 1896 | 0 | 146 | |
13
- Calculate the mean and standard deviation of \(\mathrm { CO } _ { 2 }\) emissions in the table.
[0pt]
[2 marks]
13
- (ii) Any value more than 2 standard deviations from the mean can be identified as an outlier.
Determine, using this definition of an outlier, if there are any outliers in this sample of \(\mathrm { CO } _ { 2 }\) emissions.
Fully justify your answer.
13 - Maria claims that the last line in the table must contain two errors. Use your knowledge of the Large Data Set to comment on Maria's claim.
\(14 \quad A\) and \(B\) are two events such that
$$\begin{aligned}
& \mathrm { P } ( A \cap B ) = 0.1
& \mathrm { P } \left( A ^ { \prime } \cap B ^ { \prime } \right) = 0.2
& \mathrm { P } ( B ) = 2 \mathrm { P } ( A )
\end{aligned}$$