A botanical research study finds that 45% of seeds from a specific hybrid perennial germinate within the first 10 days of being sown. The seeds are packaged in sachets of 20 for commercial sale. A sachet is selected at random.
Determine the probability that the sachet contains exactly 9 seeds that germinate within 10 days.
Determine the probability that there are at least 13 seeds in the sachet that germinate within 10 days.
Using a suitable approximation, find the probability that in a bulk tray of 200 seeds, between 80 and 105 seeds (inclusive) germinate within 10 days.
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.