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 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.