Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
The completion times, measured in minutes, for this task among workers at a large company are normally distributed with mean $32.2$ and standard deviation $9.6$.
(a)[3]
Calculate the chance that a randomly selected employee needs more than $28.6$ minutes to finish the task.
(b)[3]
$20\%$ of employees spend longer than $t$ minutes on the task. Determine the value of $t$.
(c)[4]
Determine the probability that, for a randomly chosen employee, the time needed to complete the task differs from the mean by less than $15.0$ minutes.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardisation to $Z$ with continuity correction” …