Packets of biscuits are produced by a machine. The weights $X$, in grams, of packets of biscuits can be modelled by a normal distribution where $X \sim {\text{N}}(\mu ,{\text{ }}{\sigma ^2})$. A packet of biscuits is considered to be underweight if it weighs less than 250 grams.

The manufacturer makes the decision that the probability that a packet is underweight should be 0.002. To do this $\mu$ is increased and $\sigma$ remains unchanged.

The manufacturer is happy with the decision that the probability that a packet is underweight should be 0.002, but is unhappy with the way in which this was achieved. The machine is now adjusted to reduce $\sigma$ and return $\mu$ to 253.