The volume of orange juice in a bottle produced by a filling machine is normally distributed with a mean of 505 ml and a standard deviation of 4.2 ml.
Find the probability that a randomly selected bottle has a volume of less than 498 ml.
The production manager suspects that the mean volume of juice in the bottles is lower than the specified 505 ml.
Write down the null and alternative hypotheses for the manager's suspicion.
A random sample of 25 bottles is taken and the mean volume is found to be 503 ml.
Carry out a test at the 5% significance level to see if there is evidence that the mean volume is less than 505 ml.
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.