7 The time in hours taken for clothes to dry can be modelled by the continuous random variable with probability density function given by $$f ( t ) = \begin{cases} k \sqrt { } t & 1 \leqslant t \leqslant 4
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.

1. Show that \(k = \frac { 3 } { 14 }\).
2. Find the mean time taken for clothes to dry.
3. Find the median time taken for clothes to dry.
4. Find the probability that the time taken for clothes to dry is between the mean time and the median time.