6 Each day, for many years, the maximum temperature in degrees Celsius at a particular location is recorded. The maximum temperatures for days in October can be modelled by a Normal distribution. The appropriate Normal curve is shown in Fig. 6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e9f3a5f3-210b-453d-9ff5-8518340f5689-05_761_1397_484_246}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
- Use the model to write down the mean of the maximum temperatures.
- Explain why the curve indicates that the standard deviation is approximately 3 degrees Celsius.
Temperatures can be converted from Celsius to Fahrenheit using the formula \(F = 1.8 C + 32\), where \(F\) is the temperature in degrees Fahrenheit and \(C\) is the temperature in degrees Celsius.
- For maximum temperature in October in degrees Fahrenheit, estimate
- the mean
- the standard deviation.
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Answer all the questions.
Section B (77 marks)
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\(7 \quad\) Two events \(A\) and \(B\) are such that \(\mathrm { P } ( A ) = 0.6 , \mathrm { P } ( B ) = 0.5\) and \(\mathrm { P } ( A \cup B ) = 0.85\). Find \(\mathrm { P } ( A \mid B )\).