5. A garden centre sells canes of nominal length 150 cm . The canes are bought from a supplier who uses a machine to cut canes of length \(L\) where \(L \sim \mathrm {~N} \left( \mu , 0.3 ^ { 2 } \right)\).

1. Find the value of \(\mu\), to the nearest 0.1 cm , such that there is only a \(5 \%\) chance that a cane supplied to the garden centre will have length less than 150 cm . A customer buys 10 of these canes from the garden centre.
2. Find the probability that at most 2 of the canes have length less than 150 cm . Another customer buys 500 canes.
3. Using a suitable approximation, find the probability that fewer than 35 of the canes will have length less than 150 cm .
   (6)