Erik is investigating whether the number of goals a football team scores in a game can be modelled by a binomial distribution. He uses the random variable X X\,X for the number of goals scored in a game and believes that X∼B(10,0.15)X \sim B(10, 0.15)X∼B(10,0.15).
Using Erik's model, find P(X≥3)P(X \ge 3)P(X≥3).
The team plays 38 games in a season. Using Erik's model, find the expected number of games in which the team scores no goals.
Last season the team scored no goals in 7 of its 38 games, and scored 3 or more goals in 6 of its 38 games. State, with a reason, whether your answers support Erik's model.
390 exam-style questions on AQA A Level Maths 2.4 N: Statistical distributions, covering 2.4.1 Discrete distributions and the binomial, 2.4.2 The Normal distribution (A-level only), and 2.4.3 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.