Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Josie plans to board a bus that leaves at the same fixed time each day. The time, $T$, by which Josie reaches the bus stop before departure satisfies $T \sim N(5.3, 2.1^2)$.
(i)[3]
Find the probability that Josie has to wait more than 6 minutes at the bus stop.
(ii)[3]
On $5\%$ of days Josie has to wait longer than $x$ minutes at the bus stop. Find the value of $x$.
(iii)[3]
Find the probability that Josie waits more than $x$ minutes on fewer than 3 days in 10 days.
(iv)[3]
Find the probability that Josie fails to catch the bus.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardising accurately gives $P(t>6)=P\left(z>\frac{6-5.3}{2.1}\right)$” …