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(12,0.2)X \sim B(12, 0.2)X∼B(12,0.2)
Using Erik's model, find P(X≥3)P(X \geq 3)P(X≥3)
The team play 40 games, find, to the nearest whole number, the expected number of games in which the team will score no goals.
Hence find, to the nearest whole number, the expected number of games in which the team will score 3 or more goals.
Last season the team scored no goals in 3 out of 40 matches and scored 3 or more goals in 18 out of 40 matches. Explain whether or not your answers to part (b) and (c) support Erik's model.
215 exam-style questions on Edexcel A Level Maths Statistical Distributions, covering 6.1 Probability Distributions, 6.2 The Binomial Distribution, and 6.3 Cumulative Probabilities. Each one has a worked solution and a mark scheme showing where the marks go.