A cereal manufacturer includes a collectible card in some of its cereal boxes. For a specific promotion, a card is placed in 30% of the boxes. No box contains more than 1 card. The boxes are sold in multipacks of 8 boxes.
(i) Write down a suitable distribution to model the number of cards found in a multipack. (ii) Write down one assumption required for the model.
Find the probability that in 2 randomly selected multipacks, exactly 1 multipack contains exactly 2 cards.
Find the probability that a randomly selected multipack contains at least 3 cards.
An organizer buys 100 multipacks for a school event.
Using a normal approximation, find the probability that more than 40 of these multipacks contain at least 3 cards.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.