(i) The mean \(\mu\) is estimated as the median of the data, which is the middle value of the box-and-whisker plot. From the diagram, the median is 51 km h\(^{-1}\).

(ii) To estimate the standard deviation \(\sigma\), we use the interquartile range (IQR) and the properties of the normal distribution. The IQR is the difference between the upper quartile (63 km h\(^{-1}\)) and the median (51 km h\(^{-1}\)), which is 12 km h\(^{-1}\).

For a normal distribution, the IQR corresponds to approximately 1.34896 standard deviations (since \(z = \pm 0.674\) for the quartiles). Therefore, \(\sigma\) can be estimated by:

\(\sigma = \frac{63 - 51}{0.674} = \frac{12}{0.674} \approx 17.8\)