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 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.