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'.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.