(a)[3]
The random variable $Y$ follows a normal distribution with positive mean $\mu$ and standard deviation $\frac{1}{2}\mu$. Determine the probability that a value of $Y$ chosen at random is negative.
(b)[4]
The weights of bags of rice are normally distributed, with mean $2.04\,\text{kg}$ and standard deviation $\sigma\,\text{kg}$. In a random sample of $8000$ such bags, $253$ had weight above $2.1\,\text{kg}$. Find the value of $\sigma$.