6 At a certain shop the weekly demand, in kilograms, for flour is modelled by the random variable \(X\) with probability density function given by $$f ( x ) = \begin{cases} k x ^ { - \frac { 1 } { 2 } } & 4 \leqslant x \leqslant 25
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.

1. Show that \(k = \frac { 1 } { 6 }\).
2. Calculate the mean weekly demand for flour at the shop.
3. At the beginning of one week, the shop has 20 kg of flour in stock. Find the probability that this will not be enough to meet the demand for that week.
4. Give a reason why the model may not be realistic.