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.
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.