Daniel 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(8,0.2)X \sim B(8, 0.2)X∼B(8,0.2)
Using Daniel's model, find P(X≥3)P(X \geq 3)P(X≥3)
The team play 35 games, find the expected number of games in which the team will score no goals.
Last season the team scored no goals in 6 out of 35 matches and scored 3 or more goals in 7 out of 35 matches. Explain whether or not your answers to part (a) and (b) support Daniel'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.