Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

Train journey times, measured in minutes, between Alphaton and Beeton follow a normal distribution with mean $140$ and standard deviation $12$.
(a(i))[3]

Find the probability that a randomly selected train will take less than $132$ minutes to travel between Alphaton and Beeton.

(a(ii))[3]

A randomly selected train takes more than $k$ minutes to travel between Alphaton and Beeton with probability $0.675$. Find the value of $k$.

(i)[3]

Find the probability that a randomly selected train will take less than $132$ minutes to travel between Alphaton and Beeton.

(ii)[3]

A randomly selected train takes more than $k$ minutes to travel between Alphaton and Beeton with probability $0.675$. Find the value of $k$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardising gives $P(X<132) = P\left(Z < \frac{132-140}{12}\right) = P(Z<-0.6667)$” …

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI