6 In each turn of a game, a coin is pushed and slides across a table. The distance, \(X\) metres, travelled by the coin has probability density function given by $$f ( x ) = \begin{cases} k x ^ { 2 } ( 2 - x ) & 0 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.

1. State the greatest possible distance travelled by the coin in one turn.
2. Show that \(k = \frac { 3 } { 4 }\).
3. Find the mean distance travelled by the coin in one turn.
4. Out of 400 turns, find the expected number of turns in which the distance travelled by the coin is less than 1 metre.