Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Each Saturday, one local community runs a ‘Puzzle’ event to collect funds for a new Leisure Centre. Those taking part try to finish a puzzle in the shortest possible time. Last Saturday, 600 competitors took part. The times to complete the puzzle were normally distributed with mean $32.4$ minutes and standard deviation $2.5$ minutes.
(a)[4]
What number of competitors would you expect to have times within $1.2$ minutes of the mean time?
(b)[3]
In this Saturday’s event, $60\%$ of the competitors had times below $36.0$ minutes. $9$ competitors from this Saturday’s event are chosen at random. Find the probability that at least $2$ and fewer than $8$ of these competitors had times below $36.0$ minutes.
(c)[5]
$80$ competitors from this Saturday’s event are chosen at random. Use an appropriate approximation to find the probability that more than $50$ of these competitors had times below $36.0$ minutes.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardisation, e.g. $P\left(-\frac{1.2}{2.5}<Z<\frac{1.2}{2.5}\right)$” …