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.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.