Company A produces bags of sugar. An inspector finds that on average 10% of the bags are underweight.

10 of the bags are chosen at random.

(a) Find the probability that fewer than 3 of these bags are underweight. [3]

The weights of the bags of sugar produced by company B are normally distributed with mean 1.04 kg and standard deviation 0.06 kg.

(b) Find the probability that a randomly chosen bag produced by company B weighs more than 1.11 kg. [3]

81% of the bags of sugar produced by company B weigh less than \(w\) kg.

(c) Find the value of \(w\). [3]