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
(i)
Two randomly selected male are taller than twice a randomly selected female.
(ii)
A randomly selected male student is taller than a randomly selected female student by at least $20$ cm.
(iii)
The difference in height between a randomly selected male and a female is more than $30$ cm.
(iv)
The heights of two randomly selected female students both exceed $1.5$ m.
(v)
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).
