Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
In a cycling event, the completion times for the course are represented using a normal distribution with mean $62.3$ minutes and standard deviation $8.4$ minutes.
(a)[2]
Find the probability that a cyclist selected at random records a time below $74$ minutes.
(b)[4]
Find the probability that all $4$ randomly chosen cyclists have times between $50$ and $74$ minutes.
(c)[5]
In another cycling event, the times are also modelled by a normal distribution. $23\%$ of the cyclists record times below $36$ minutes and $10\%$ of the cyclists record times above $54$ minutes. Find estimates for the mean and standard deviation of this distribution.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct standardising: $P(X<74)=P\left(Z<\frac{74-62.3}{8.4}\right)$” …