4 A mathematical puzzle is given to a large number of students. The times taken to complete the puzzle are normally distributed with mean 14.6 minutes and standard deviation 5.2 minutes.
- In a random sample of 250 of the students, how many would you expect to have taken more than 20 minutes to complete the puzzle?
All the students are given a second puzzle to complete. Their times, in minutes, are normally distributed with mean \(\mu\) and standard deviation \(\sigma\). It is found that \(20 \%\) of the students have times less than 14.5 minutes and \(67 \%\) of the students have times greater than 18.5 minutes. - Find the value of \(\mu\) and the value of \(\sigma\).