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.