(a)[3]
The mean time for a random sample of $n$ of these journeys was calculated. A $94\%$ confidence interval for the population mean time was then obtained, and its width was $1.4076$ minutes, correct to $4$ decimal places. Find the value of $n$.
(b)[1]
A passenger recorded the times for $50$ journeys selected at random in January, February and March. Give a reason why this sample is unsuitable for use in finding a confidence interval for the population mean time.
(c)[2]
A researcher drew $4$ random samples and found a $94\%$ confidence interval for the population mean from each one. Find the probability that exactly $3$ of these confidence intervals include the true population mean.