A construction supplier provides two types of steel components: girders and industrial bolts. The mass of each component is normally distributed. A girder has a mean mass of 520 kg and a standard deviation of 8 kg. An industrial bolt has a mean mass of 60 kg and a standard deviation of 3 kg.
One girder and 8 industrial bolts are selected at random. Find the probability that the mass of the girder exceeds the combined mass of the 8 industrial bolts.
A single girder and a single bolt are selected at random. Determine the probability that the mass of the girder is less than 8 times the mass of the single bolt.
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.