Q19 · 2025 · Technology-activeComplex unfamiliar6 marks
QUESTION 19 (6 marks)
A scientist is gathering data on two species of horned beetle, species A and B. Horn length is a method of distinguishing the species.
Species A horn lengths are normally distributed with a mean of 20 mm and a standard deviation of 2 mm.
It is known that 14.6% of species B beetles have horns shorter than 18 mm.
In the particular population the scientist is studying, 30% of the beetles are species B and 70% are species A.
The scientist captures a beetle with a horn length shorter than 18 mm.
Determine the probability that the beetle is from species A.
WORKED SOLUTION
6 marksQCAA guide · typeset solution
ANSWER
(71.7%).
Worked solution
Let denote species A and denote species B.
For species A, use the normal distribution with and :
The total proportion of beetles with horns shorter than 18 mm is
Using conditional probability,
correctly determines the proportion of species A beetles with horn length shorter than 18 mm
correctly determines a method to find the proportion of the total population with horn length shorter than 18 mm
determines the proportion of all beetles with horn length shorter than 18 mm
uses conditional probability to solve the problem
determines the probability the captured beetle is from species A
shows logical organisation
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