normal interval probability

Practise normal interval probability with an original VectorPaths question, worked explanation and related VCE Methods practice.

2 practice marks

Original practice question

$X$ is normally distributed with mean 60 and standard deviation 8. Find $P(52\leq X\leq 68)$ to four decimal places.

Worked explanation

• Standardise both endpoints

  $z_1=(52-60)/8=-1$; $z_2=(68-60)/8=1$.

• Subtract cumulative probabilities

  $\Phi(1)-\Phi(-1)=0.6827$.

Probability $=0.6827$.

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