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 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.