State the conditions under which a normal distribution may be used to approximate a binomial distribution.
A botanist is testing the germination rate of a new hybrid seed variety. The probability of any individual seed germinating under standard conditions is 0.45.
For a batch of 20 seeds, determine the modal number of seeds that germinate. Justify your answer.
The random variable S S\,S represents the total number of seeds that germinate when 60 of these seeds are planted.
Find P(S<22)P(S < 22)P(S<22).
Given that exactly 12 seeds germinate from a specific batch of 20, find the probability that exactly 8 of these germinated from the first 14 seeds planted in that batch.
In a large-scale agricultural trial, 500 seeds are planted. Using a suitable approximation, find the probability that at most 235 seeds germinate.
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.