Inverse normal percentile and interpretation

Practise inverse normal percentile and interpretation with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

Scores are modelled by a normal distribution with mean 70 and standard deviation 8. The highest 10% qualify for an award. (a) State the cumulative probability used for the cutoff. [1 marks] (b) Find c to two decimal places. [2 marks]

Worked explanation

• Part (a)

  The top 10% are above the threshold c, so $P(X\leq c)=0.90$.

• Part (b)

  The standard normal 90th percentile is $1.281552$. Therefore $c=70+8(1.281552)=80.25$.

(a) $0.90$.; (b) $80.25$.

Original VectorPaths practice; not an official VCAA question or marking rubric.