Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
A mathematical puzzle is presented to a large group of students. The completion times are normally distributed, with mean $14.6$ minutes and standard deviation $5.2$ minutes.
(a)[4]
From a random sample of $250$ students, what number would you expect to have spent more than $20$ minutes completing the puzzle?
(b)[5]
Every student is assigned a second puzzle to finish. Their times, measured in minutes, are normally distributed with mean $\mu$ and standard deviation $\sigma$. It is established that $20\%$ of the students have times below $14.5$ minutes and $67\%$ of the students have times above $18.5$ minutes. Determine the value of $\mu$ and the value of $\sigma$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardisation $P\left(Z>\dfrac{20-14.6}{5.2}\right)$.” …