Noah is investigating whether the number of faulty items in a batch can be modelled using a binomial distribution. He uses the random variable X X\,X to denote the number of faulty items in a batch of 6 items and believes X∼B(6,0.25)X \sim B(6, 0.25)X∼B(6,0.25)
Using Noah's model, find P(X≥3)P(X \geq 3)P(X≥3)
A factory produces 32 batches. Find the expected number of batches containing no faulty items.
Of the 32 batches produced last month, 6 contained no faulty items and 5 contained 3 or more faulty items. Explain whether or not your answers to parts (a) and (b) support Noah'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.