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.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.