An entomologist studies the wingspans of a specific species of hawk moth. The wingspans, SSS millimetres, are normally distributed with a mean of 42 mm42\text{ mm}42 mm and a standard deviation of 6 mm6\text{ mm}6 mm.
Estimate the proportion of these moths that have a wingspan greater than 51 mm51\text{ mm}51 mm.
The entomologist classifies the moths into three categories: Narrow, Average, and Wide, such that there is an equal proportion of moths (exactly 13\frac{1}{3}31) in each category.
Determine the range of wingspans that defines the 'Average' category.
A moth is selected at random from the 'Wide' category.
Find the probability that this moth's wingspan is less than 48 mm48\text{ mm}48 mm.
A researcher collects a random sample of 3 moths from the population.
Find the probability that there is exactly one moth from each of the three categories.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.