An environmental scientist finds that the probability of a soil sample from a specific industrial region containing high levels of lead is 0.08. Samples are collected independently.
In a random selection of 50 soil samples, determine the probability that at least 7 samples contain high levels of lead.
A construction company analyzes a large batch of 600 soil samples. The entire site undergoes a mandatory decontamination process if more than 60 samples in the batch are found to have high lead levels.
Use a suitable approximation to estimate the probability that the site undergoes the decontamination process.
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.