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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.