A space agency monitors the deployment of a large constellation of n n\,n small satellites. The number of satellites, SSS, that successfully reach their intended altitude in a single deployment phase is modeled by the discrete random variable S∼B(n,p)S \sim \text{B}(n, p)S∼B(n,p). The mean number of successful deployments is 80.
State the variance of S S\,S in terms of ppp.
A normal distribution is used as an approximation for SSS. Using this approximation and a continuity correction, it is found that P(S≥92)=0.0301P(S \ge 92) = 0.0301P(S≥92)=0.0301 to 3 significant figures.
Show that 80−80p=6.117\sqrt{80 - 80p} = 6.11780−80p=6.117 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.