7. A machine fills bottles with water. The volume of water delivered by the machine to a bottle is \(X \mathrm { ml }\) where \(X \sim \mathrm {~N} \left( \mu , \sigma ^ { 2 } \right)\) One of these bottles of water is selected at random. Given that \(\mu = 503\) and \(\sigma = 1.6\)

1. find
   1. \(\mathrm { P } ( X > 505 )\)
   2. \(\mathrm { P } ( 501 < X < 505 )\)
2. Find \(w\) such that \(\mathrm { P } ( 1006 - w < X < w ) = 0.9426\) Following adjustments to the machine, the volume of water delivered by the machine to a bottle is such that \(\mu = 503\) and \(\sigma = q\) Given that \(\mathrm { P } ( X < r ) = 0.01\) and \(\mathrm { P } ( X > r + 6 ) = 0.05\)
3. find the value of \(r\) and the value of \(q\)