(a)[3]
Determine the probability that a bag of rice chosen at random from those produced by Anders has a weight between $1.98\text{ kg}$ and $2.03\text{ kg}$.
(b)[4]
For bags of rice produced by Binders, the weights follow a normal distribution with mean $2.55\text{ kg}$ and standard deviation $\sigma\text{ kg}$. In a random sample of $5000$ of these bags, $134$ had weights greater than $2.6\text{ kg}$. Determine the value of $\sigma$.