(c) The height of a door of the library of a certain local university is 1.830m. The heights of the students of the university are normally distributed with a mean of 1.730 m and standard deviation of 0.064 m. (i) Find the proportion of students that will be taller than the door frame. (ii) Find the height of a door frame such that one students in a thousand will be taller than the door frame height. (iii) It is known that the female students outnumber the male students in the ratio 6:4 in that university and the proportion of female students taller than the door frame is 0.0162. Find the proportion of students for whom a door frame of height 1.830 m would be too low.

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