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~ N(u, oʻ). A packet of biscuits is
considered to be underweight if it weighs less than 250 grams.
(a) Given that u = 253 and o=1.5 find the probability that a randomly chosen packet of
biscuits is underweight.
The manufacturer makes the decision that the probability that a packet is underweight should
be 0.002. To do this u is increased and o remains unchanged.
(b)
Calculate the new value of u giving your answer correct to two decimal places.
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 o and return u to 253.
(c)
Calculate the new value of o.