Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The duration, in minutes, of one particular daily train journey follows a normal distribution with standard deviation $5.8$. From a random sample of 20 days, the journey times were recorded and the sample mean journey time was $81.5$ minutes.
(a)[3]
Calculate a $98\%$ confidence interval for the population mean journey time.
(b)[1]
Explain briefly whether the statement ‘The times for $98\%$ of these journeys are likely to be within the confidence interval.’ is true or not.
(c)[2]
Given that at least one of these intervals contains the population mean, find the probability that both intervals contain the population mean.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the correct confidence interval form $81.5 \pm z\,\frac{5.8}{\sqrt{20}}$ (any $z$).” …