Maya is investigating whether the number of goals scored by a football team in a game can be modelled using a binomial distribution. She 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 Maya's model, find P(X≥3)P(X \geq 3)P(X≥3)
The team play 45 games. Find the expected number of games in which the team will score no goals.
Last season the team scored no goals in 8 out of 45 matches and scored 3 or more goals in 9 out of 45 matches. Explain whether or not your answers to parts (a) and (b) support Maya's model.
57 exam-style questions on Edexcel AS 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.