5. A drinks machine dispenses lemonade into cups. It is electronically controlled to cut off the flow of lemonade randomly between 180 ml and 200 ml . The random variable \(X\) is the volume of lemonade dispensed into a cup.

1. Specify the probability density function of \(X\) and sketch its graph.
2. Find the probability that the machine dispenses
   1. less than 183 ml ,
   2. exactly 183 ml .
3. Calculate the inter-quartile range of \(X\).
4. Determine the value of \(x\) such that \(\mathrm { P } ( X \geq x ) = 2 \mathrm { P } ( X \leq x )\).
5. Interpret in words your value of \(x\).