Standardise and calculate an interval probability

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

3 practice marks

Original practice question

X is normally distributed with mean 50 and standard deviation 6. (a) Standardise the endpoints 44 and 56. [1 marks] (b) Find $P(44<X<56)$ to four decimal places. [2 marks]

Worked explanation

• Part (a)

  Use $Z=(X-50)/6$: the endpoints become $(44-50)/6=-1$ and $(56-50)/6=1$.

• Part (b)

  $P(-1<Z<1)=\Phi(1)-\Phi(-1)=0.6827$. A continuous variable has zero probability at each endpoint.

(a) $-1$ and $1$.; (b) $0.6827$.

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