The amount of water W W\,W ml placed in a bottle is Normally distributed with mean 500 ml. It is known that P(W>504)=0.30P(W>504)=0.30P(W>504)=0.30.
Find the standard deviation of WWW.
Find k k\,k such that P(k<W<505)=0.45P(k<W<505)=0.45P(k<W<505)=0.45. The machine is adjusted and its population standard deviation becomes 6 ml. A manager believes that the population mean is now less than 500 ml. A random sample of 20 bottles has mean 498.1 ml.
Test the manager's belief at the 5% 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.