The weight, \(X\) grams, of soup put in a tin by machine \(A\) is normally distributed with a mean of 160 g and a standard deviation of 5 g .
A tin is selected at random.
Find the probability that this tin contains more than 168 g .
The weight stated on the tin is \(w\) grams.
Find \(w\) such that \(\mathrm { P } ( X < w ) = 0.01\)
The weight, \(Y\) grams, of soup put into a carton by machine \(B\) is normally distributed with mean \(\mu\) grams and standard deviation \(\sigma\) grams.
Given that \(\mathrm { P } ( Y < 160 ) = 0.99\) and \(\mathrm { P } ( Y > 152 ) = 0.90\) find the value of \(\mu\) and the value of \(\sigma\).