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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.