The volume of liquid, in ml, in a bottle of water is normally distributed with mean μ\muμ and standard deviation 6.46.46.4. Given that 5%5\%5% of bottles contain less than 490 ml490\text{ ml}490 ml, find:
the value of μ\muμ to two decimal places.
the percentage of bottles that contain more than 510 ml510\text{ ml}510 ml.
The bottling machine is recalibrated so that the volume of liquid is normally distributed with mean 500500500 and standard deviation σ\sigmaσ.
Given that 95%95\%95% of bottles contain between 495 ml495\text{ ml}495 ml and 505 ml505\text{ ml}505 ml, find the value of σ\sigmaσ.
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.