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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.