The amount of coffee, XXX ml, dispensed into a cup by machine PPP is normally distributed with a mean of 250 ml250\text{ ml}250 ml and a standard deviation of 8 ml8\text{ ml}8 ml.
Find the probability that a randomly selected cup contains more than 262 ml262\text{ ml}262 ml.
A 'regular' size is defined such that only 2%2\%2% of cups contain less than v mlv\text{ ml}v ml. Find the value of vvv.
The amount of coffee, YYY ml, dispensed by machine QQQ is normally distributed with mean μ\muμ and standard deviation σ\sigmaσ.
Given that P(Y<240)=0.05P(Y < 240) = 0.05P(Y<240)=0.05 and P(Y<265)=0.98P(Y < 265) = 0.98P(Y<265)=0.98, find the value of μ\muμ and 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.