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(10,0.15)X \sim B(10, 0.15)X∼B(10,0.15)
Using Erik's model, find P(X≥3)P(X \geq 3)P(X≥3)
The team play 38 games, find the expected number of games in which the team will score no goals.
Last season the team scored no goals in 7 out of 38 matches and scored 3 or more goals in 6 out of 38 matches. Explain whether or not your answers to part (a) and (b) support Erik's model.