An agricultural scientist is researching a rare hybrid orchid. The probability that a single seed of this orchid will successfully germinate in specific soil conditions is 0.35. A random batch of 60 seeds is planted. Let the random variable SSS represent the number of seeds in the batch that successfully germinate.
Determine (i) P(S=25)P(S = 25)P(S=25) (ii) P(S<20)P(S < 20)P(S<20) (iii) the smallest value of kkk such that P(S≤k)>0.85P(S \le k) > 0.85P(S≤k)>0.85
A much larger random sample of 800 seeds is planted in the same soil conditions.
(i) Using a suitable normal approximation, find the probability that no more than 260 of these 800 seeds germinate. (ii) Justify why a normal approximation is appropriate in part (b)(i).
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.