Worked Example 7

The heights, in metres, of female and male students in a school follow normal distributions with the following data.

Find the probability that

1. Two randomly selected male are taller than twice a randomly selected female.
2. A randomly selected male student is taller than a randomly selected female student by at least \(20\) cm.
3. The difference in height between a randomly selected male and a female is more than \(30\) cm.
4. The heights of two randomly selected female students both exceed \(1.5\) m.
5. The total height of two randomly selected female students is more than \(3\) m.

Comment on the difference in answers for part (iv) and (v).