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 100 and standard deviation 15. Find $P(85\leq X\leq 130)$ to four decimal places.

Worked explanation

• Standardise both endpoints

  $z_1=(85-100)/15=-1$; $z_2=(130-100)/15=2$.

• Subtract cumulative probabilities

  $\Phi(2)-\Phi(-1)=0.8186$.

Probability $=0.8186$.

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