Questions 3 (9 marks)

X and Y are two schools with the same number of students The daily reading times (in minutes) of the students in each school are assumed to be normally distributed. In school X, the mean daily reading time is 56.09 minutes with a standard deviation 6.41 minutes. In school Y, 1.5% of the students read less than 48 minutes daily while 1.7% read more than 72 minutes.

(a) Determine the mean and standard deviation of the daily reading times of the students in school Y.

(4 marks)

(b) Students reading T minutes or more daily will be awarded. What should be the least value of T be so that no more than 33% of students are awarded in each school. Give your answer in integral minutes.

(5 marks)