Leah is investigating whether the number of successful penalty kicks taken by a player in a sequence can be modelled using a binomial distribution. She uses the random variable X X\,X to denote the number of successful penalty kicks in a sequence of 12 attempts and believes X∼B(12,0.1)X \sim B(12, 0.1)X∼B(12,0.1)
Using Leah's model, find P(X≥3)P(X \geq 3)P(X≥3)
The player completes 50 sequences of 12 penalty kicks. Find the expected number of sequences in which the player scores no successful penalty kicks.
In the 50 sequences last season, the player had no successful penalty kicks in 14 sequences and scored 3 or more successful penalty kicks in 6 sequences. Explain whether or not your answers to parts (a) and (b) support Leah'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.