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 (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.