Conditional normal probability

Practise conditional normal 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 100 and standard deviation 10. (a) Find $P(X>100)$. [1 marks] (b) Find $P(X>110\mid X>100)$ to four decimal places. [2 marks]

Worked explanation

• Part (a)

  By symmetry about the mean, half the distribution lies above 100.

• Part (b)

  The event $X>110$ is contained in $X>100$. Hence the conditional probability is $[1-\Phi(1)]/0.5=0.3173$.

(a) $1/2$.; (b) $0.3173$.

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