A marine biologist uses an automated submersible to survey a deep-sea ridge. The probability of the submersible capturing an image of a rare bioluminescent jellyfish, JJJ, during any single 10-minute observation segment is 0.18.
The biologist conducts a short-range mission consisting of 25 observation segments. Determine the probability that fewer than 3 images of the jellyfish are captured.
In a subsequent large-scale longitudinal study involving 400 observation segments, use a suitable approximation to estimate the probability that the biologist captures more than 80 images of the jellyfish.
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.