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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, 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.