A botanist observes that the number of seeds, SSS, that germinate in a large nursery plot follows a binomial distribution S∼B(n,p)S \sim \text{B}(n, p)S∼B(n,p). The expected number of germinated seeds is 200.
State the variance of SSS in terms of ppp.
A normal distribution is used as an approximation for SSS. Using this approximation and a continuity correction, the probability that 180 or fewer seeds germinate is approximately 0.0384.
Show that 200−200p=11.02\sqrt{200 - 200p} = 11.02200−200p=11.02 to 4 significant figures.
Hence find the value of ppp, giving your answer to 2 significant figures.
Practise Edexcel A Level Maths Approximating a Binomial Distribution with exam-style questions for A Level Maths. 68 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
