Statistics Question

In a factory, the packets of oats produced are supposed to contain 1kg of oats each. Over a long period it has been found that the weights of the contents of the packets of oats produced in the factory are normally distributed with mean 1.02 kg and standard deviation 0.009kg.
Calculate, to one demical place, the percentage of packets in the production which have contents whose weights are not within 0.005kg of the required 1kg.

I'd be grateful for a solution.

Reply 1

generalebriety

Let X be the weight of one particular packet. Then X~N(1.02, 0.009^2), and so Z = (X - 1.02)/0.009. Work out P(0.995 < X < 1.005), and this will give you the percentage of packets whose weights are within 0.005kg. Then subtract it from 1... you get the idea.