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(10,0.20)X \sim B(10, 0.20)X∼B(10,0.20)
Using Erik's model, verify that P(X≥3)=0.322P(X \geq 3) = 0.322P(X≥3)=0.322 to 3 significant figures.
The team play 38 games, verify that the expected number of games in which the team will score no goals is 4, to the nearest whole number.
Last season the team scored no goals in 4 out of 38 matches and scored 3 or more goals in 12 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.