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).
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.