4 A certain train journey takes place every day throughout the year. The time taken, in minutes, for the journey is normally distributed with variance 11.2.
- The mean time for a random sample of \(n\) of these journeys was found. A \(94 \%\) confidence interval for the population mean time was calculated and was found to have a width of 1.4076 minutes, correct to 4 decimal places.
Find the value of \(n\).
- A passenger noted the times for 50 randomly chosen journeys 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.
- A researcher took 4 random samples and a \(94 \%\) confidence interval for the population mean was found from each sample.
Find the probability that exactly 3 of these confidence intervals contain the true value of the population mean.