An automated agricultural research system monitors large batches of seedlings for a rare genetic mutation. This mutation occurs independently in each seedling with a probability of 0.08.
Determine the probability that in a randomly selected batch of 25 seedlings, exactly 3 will possess this mutation.
Batches are grouped into larger delivery trays, each containing 50 seedlings. A quality control inspector selects 5 of these trays at random.
Find the probability that exactly two of these trays will contain more than 6 seedlings with the mutation.
A high-capacity growing facility contains n n\,n seedlings of a different strain, where the probability of the mutation is 0.2.
Using a normal approximation, the probability that this facility contains more than 91 seedlings with the mutation is 0.0749.
Find the value of nnn.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.