The weights of a population of adult males are normally distributed with mean μ\muμ kg and standard deviation σ\sigmaσ kg. It is known that 10% of the males weigh more than 95 kg and 2.5% weigh less than 65 kg.
Sketch a diagram to show the distribution of weights represented by this information.
Show that μ=95−1.2816σ\mu = 95 - 1.2816\sigmaμ=95−1.2816σ.
Obtain a second equation involving μ\muμ and σ\sigmaσ, and hence find the value of μ\muμ and the value of σ\sigmaσ to 2 decimal places.
Find the probability that a male chosen at random from the population weighs more than 80 kg.
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.