A student arrives at a school X minutes after 08:00, where X may be assumed to be normally distributed. On a particular day it is observed that 40 % of the students arrive before 08:30 and 90 % arrive before 08:55. Required:
a. Find the mean and standard deviation of X.
b. The school has 1200 students and classes start at 09:00. Estimate the number of students who will be late on that day.
c. Maelis had not arrived by 08:30. Find the probability that she arrived late.