An urban transport survey finds that 22% of commuters in a specific metropolitan area utilize a bike-sharing application for their daily travel.
A random sample of 45 commuters is selected. Determine the probability that at most 8 of these commuters utilize the bike-sharing application.
A second, larger random sample of 250 commuters is selected. Using a normal approximation, estimate the probability that the number of commuters in this sample who utilize the bike-sharing application is fewer than 50.
67 exam-style questions on OCR A Level Maths 2.4.4 Mean and variance of the binomial (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.