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.
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.