The weights, in kg, of male travelers at an airport follow a normal distribution with mean 82 and standard deviation 7. The weights of female travelers follow a normal distribution with mean 68 and standard deviation 6.
A male traveler and a female traveler are chosen at random.
Find the probability that the male traveler weighs more than the female traveler.
Five male travelers and five female travelers are chosen at random to board a small shuttle.
Find the probability that their total weight is greater than 775 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.