A food processing plant packs cereal into boxes with a target mean weight of 500g. A quality control inspector believes the machine is underfilling the boxes. A random sample of 100 boxes is weighed, giving the following statistics:
n=100∑x=49910∑x2=24912581 n = 100 \quad \sum x = 49910 \quad \sum x^2 = 24912581 n=100∑x=49910∑x2=24912581Find the mean and standard deviation of the sample.
Carry out a hypothesis test to test the inspector's belief at the 1% significance level. State your assumptions clearly.
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.