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'.
