Q14 · 2021 · Technology-activeSimple familiar7 marks
QUESTION 14 (7 marks)
The heights of students at School A are normally distributed with a mean of 165 cm and a standard deviation of 15 cm.
a)[1 mark]
Determine the probability that a student chosen at random from School A is shorter than 180 cm.
b)[3 marks]
Determine the minimum integer value of the height of a student who is in the top 2% of this distribution.
c)[3 marks]
The heights of students at School B are also normally distributed. A student at School B has the same height as the height determined in Question 14b) but their corresponding -score is 3. Determine which student’s height ranks higher in terms of percentile for their school.
WORKED SOLUTION
7 marksQCAA guide · typeset solution
ANSWER
a) ; b) cm; c) the student in School B
Worked solution
a) Using a GDC, .
b) The top 2% cutoff is , so the minimum integer height is cm.
c) For School A, Therefore the student in School B ranks higher.
correctly determines the probability
correctly uses an appropriate mathematical representation
correctly determines the lowest decimal height
determines lowest whole height
determines z-score for student in School A
provides statement to justify decision
determines higher ranked student
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