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.
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.