Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The crossing time, measured in minutes, for a ferry to travel across a lake follows a normal distribution with mean $85$ and standard deviation $6.8$.
(i)[3]

Find the probability that, on a randomly selected occasion, the ferry takes between $79$ and $91$ minutes to cross the lake.

(ii)[3]

Over a long period, it is observed that $96\%$ of ferry crossings last longer than a particular time $t$ minutes. Find the value of $t$.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the standardisation formula to obtain $P(79 < X < 91)$, for example $P\left(\frac{79-85}{6.8} < Z < \frac{91-85}{6.8}\right)$” …

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