A machine fills bottles with water. The amount of water in each bottle, W W\,W ml, is normally distributed with mean 500 ml. Given that 30% of bottles contain more than 504 ml
Find the value of 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 so that the standard deviation of the amount of water in each bottle is now 6 ml. Following the adjustments the company manager now believes that the mean amount of water in each bottle is less than 500 ml. She takes a random sample of 20 bottles and finds the mean amount of water to be 498.1 ml. Test the company manager's belief at the 5% significance level. You should state your hypotheses 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.