Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A random sample of $50$ roads from one region had their lengths measured. From these results, a $95\%$ confidence interval for the mean length, in metres, of all roads in this region was obtained as $[245, 263]$.
(a)[1]
Find the mean length of the $50$ roads in the sample.
(b)[2]
Calculate an estimate of the standard deviation of road lengths in this region.
(c)[1]
It is now stated that the lengths of roads in this region are normally distributed. State, with a reason, whether this would alter your calculation in part (b).
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct sample mean is $254\text{ m}$.” …