3. A machine pours oil into bottles. It is electronically controlled to cut off the flow of oil randomly between 100 ml and \(k \mathrm { ml }\), where \(k > 100\). It is equally likely to cut off the flow at any point in this range. The random variable \(X\) is the volume of oil poured into a bottle. Given that \(\mathrm { P } ( 102 \leqslant X \leqslant k ) = \frac { 2 } { 3 }\)

1. show that \(k = 106\)
2. Find the probability that the volume of oil poured into a bottle is
   1. less than 105 ml ,
   2. exactly 105 ml .
3. Write down the value of \(\mathrm { E } ( X )\)
4. Find the 15th percentile of this distribution.
5. Determine the value of \(x\) such that \(3 \mathrm { P } ( X \leqslant x - 1.5 ) = \mathrm { P } ( X \geqslant x + 1.5 )\)