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.