Erik is investigating whether the number of goals scored by a football team in a game can be modelled using a binomial distribution. He uses the random variable X X\,X to denote the number of goals scored in a game and believes X∼B(10,0.15)X \sim B(10, 0.15)X∼B(10,0.15)
Using Erik's model, find P(X≥3)P(X \geq 3)P(X≥3)
The team play 38 games, find the expected number of games in which the team will score no goals.
Last season the team scored no goals in 7 out of 38 matches and scored 3 or more goals in 6 out of 38 matches. Explain whether or not your answers to part (a) and (b) support Erik's model.
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.