In a large residential district, it is estimated that 22% of households have installed solar panels.
State two assumptions required to model the number of households with solar panels in a random sample of size nnn using a binomial distribution.
Using this model, find the probability that exactly 4 households have solar panels in a random sample of 18 households.
Calculate the mean and the variance of the number of households with solar panels in a random sample of 250 households.
A regional council inspects a random sample of 250 households. The district is classified as 'Eco-Leading' if more than 62 households in the sample have installed solar panels.
Using a suitable approximation, find the probability that the district will be classified as 'Eco-Leading'.
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.