Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
For mathematics lectures at this college, the duration in minutes has mean $\mu$ and standard deviation $8.3$.
(a)[3]
A random sample of $85$ lectures had a combined duration of $4590$ minutes. Calculate a $95\%$ confidence interval for $\mu$.
(b)[2]
At the college, the duration in minutes of history lectures has mean $m$ and standard deviation $s$. From a random sample of $100$ history lectures, a $95\%$ confidence interval for $m$ was found to have width $2.8$ minutes. Find the value of $s$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write the confidence interval as $\dfrac{4590}{85} \pm z\dfrac{8.3}{\sqrt{85}}$” …