Describe the Central Limit Theorem and state the condition usually required for its application.
A boutique apiary produces jars of organic honey. The mass of honey in a jar is a random variable with a known population standard deviation of 4.5 g. A trading standards officer selects a random sample of 81 jars and records the total mass of honey as ∑m=40,230 g\sum m = 40,230\text{ g}∑m=40,230 g.
Determine a 95% confidence interval for the population mean mass, μ\muμ, of honey in the jars.
Explain why the Central Limit Theorem was necessary for the calculation in part (b).
The apiary labels the jars as containing an average of 500 g of honey.
Using your confidence interval, evaluate the suggestion that the apiary is under-filling the jars. Justify your answer.
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.