3 At a factory, flour is packed into bags. A model for the mass in grams of flour packed into each bag is \(1500 + X\), where \(X\) is a continuous random variable with probability density function $$f ( x ) = \left\{ \begin{array} { c c } k x ( 6 - x ) & 0 \leq x \leq 6
0 & \text { elsewhere, } \end{array} \right.$$ where \(k\) is a constant.

1. Show that \(k = \frac { 1 } { 36 }\).
2. Find the probability that a randomly selected bag of flour contains 1505 grams of flour or more.
3. Find
   • the mean of \(X\),
   • the standard deviation of \(X\).