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.
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.