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(8,0.20)X \sim B(8, 0.20)X∼B(8,0.20). Using Erik's model, P(X≥3)=0.203P(X \geq 3)=0.203P(X≥3)=0.203 and the expected number of games in which the team will score no goals over 38 games is 6.375...≈6 6.375... \approx 6\,6.375...≈6 games.
Last season the team scored no goals in 6 out of 38 matches and scored 3 or more goals in 8 out of 38 matches. Explain whether or not your answers to part (a) and (b) 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.