The random variable \(Y\) is normally distributed with positive mean \(\mu\) and standard deviation \(\frac { 1 } { 2 } \mu\). Find the probability that a randomly chosen value of \(Y\) is negative.
The weights of bags of rice are normally distributed with mean 2.04 kg and standard deviation \(\sigma \mathrm { kg }\). In a random sample of 8000 such bags, 253 weighed over 2.1 kg . Find the value of \(\sigma\). [4]