The mass of flour in bags packed by a factory is normally distributed with a mean of 1500 g and a standard deviation of 25 g.
Find the probability that a randomly selected bag of flour has a mass of less than 1450 g.
A quality inspector believes the bagging machine is under-filling and the mean mass is less than 1500 g.
State the null and alternative hypotheses for this test.
A random sample of 16 bags is weighed and the mean mass is found to be 1485 g.
Test the inspector's belief at the 1% significance level.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.