(a) The Department of Education found that only 55 percent of students attend school in a remote community. If a random sample of 500 children is selected, what is the approximate probability that at least 250 children will attend school? Use normal approximation of the binomial distribution. 1.5 marks ( b ) A hotel chain found that 120 out of 225 visitor who booked a room cancelled their bookings prior to the 24hr no refund period. Determine whether there is evidence that the population proportion of visitors who book their stay and cancel their bookings prior to the no refund period is less than 50% at a 1% confidence level. 1.5 marks (c) The Queensland education department surveyed 1000 parents to assess those with having financial hardship. It was determined that 19% of the parents suffered some financial hardship of which 10% could not afford the full cost of their childs education. Construct a 99% confidence interval for the proportion of parents who are suffering financial hardhip and cannot afford the full cost of their child's education. 1 mark