- 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 \(\sigma = 1.6\)
- find
- \(\mathrm { P } ( X > 505 )\)
- \(\mathrm { P } ( 501 < X < 505 )\)
- 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 \(\mathrm { P } ( X > r + 6 ) = 0.05\)
- find the value of \(r\) and the value of \(q\)
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