6 The length \(L\) of a particular type of fence panel is Normally distributed with mean 179.2 cm and standard deviation 0.8 cm . You should assume that the lengths of individual fence panels are independent of each other.
- Find the probability that the length of a randomly chosen fence panel is at least 180 cm .
- Find the probability that the total length of 5 randomly chosen fence panels is less than 895 cm .
The width \(W\) of a fence post is Normally distributed with mean 9.8 cm and standard deviation 0.3 cm . A straight fence is constructed using 6 posts and 5 panels with no gaps between them.
Fig. 6 shows a view from above of the first two posts, the first panel and the start of the second panel. You should assume that the lengths of fence panels and widths of fence posts are independent.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4caa7409-cb32-41da-ad64-012a45753296-6_213_1522_934_244}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure} - Determine the probability that the total length of the fence, including the posts, is less than 9.5 m .
- State another assumption that is necessary for the calculation of the probability in part (c) to be valid.