3. A film-buff is interested in how long it takes for the credits to roll at the end of a movie. She takes a random sample of 20 movies from those that she has bought on DVD and finds that the credits on these films last for a total of 46 minutes and 15 seconds
- Assuming that the time for the credits to roll follows a Normal distribution with a standard deviation of 23 seconds, use her data to calculate a \(90 \%\) confidence interval for the mean time taken for the credits to roll.
(5 marks) - Find the minimum number of movies she would need to have included in her sample for her confidence interval to have a width of less than 10 seconds.
(5 marks) - Explain why her sample might not be representative of all movies.