- Scaffolding poles come in two sizes, long and short. The length \(L\) of a long pole has the normal distribution \(\mathrm { N } \left( 19.6,0.6 ^ { 2 } \right)\). The length \(S\) of a short pole has the normal distribution N(4.8, 0.32). The random variables \(L\) and \(S\) are independent.
A long pole and a short pole are selected at random.
- Find the probability that the length of the long pole is more than 4 times the length of the short pole. Show your working clearly.
Four short poles are selected at random and placed end to end in a row. The random variable \(T\) represents the length of the row.
- Find the distribution of \(T\).
- Find \(\mathrm { P } ( | L - T | < 0.2 )\)