A factory produces a large batch of glass beads, of which 8% are found to have minor surface imperfections. A random sample of 50 beads is selected and the number of imperfect beads is recorded.
Find the probability that there are at most 5 imperfect beads in this sample.
A second random sample of 50 beads is selected and the number of imperfect beads is recorded.
Using a Poisson approximation, estimate the probability that the total number of imperfect beads in the combined sample of size 100 is fewer than 11.
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.