The mass of sugar in a packet, in grams, is modelled by a normal distribution with mean 1000 g and standard deviation 20 g.
Using this model, find the probability that a randomly chosen packet contains more than 1035 g of sugar. Give your answer to 3 significant figures.
Find the mass of sugar that is exceeded by 5% of packets. Give your answer to 1 decimal place.
A quality control inspector suspects that the filling machine is now overfilling, so that the mean mass is greater than 1000 g. A random sample of 25 packets is taken, and the total mass of sugar in the sample is 25 250 25\,250\,25250 g.
Stating your hypotheses clearly, test the inspector's suspicion at the 5% significance level. You may assume that the standard deviation is still 20 g.