The height of student in a lecture, follows normal distribution with mean 179 cm and variance 20 cm².

Use Python programming language to

(a) Find the probability that a randomly selected student is taller than 185cm.

(b) Find the lower quartile Q₁, upper quartile Q₃ and IQRstudent's height in the lecture.

(c) The lecture has 900 students. The basketball team coach would like to invite students in the lecture who is taller than Q₃ + 1.5IQRto join the team and each student will have $100 joining fee. Estimate the proportion of students will be invited and the expected amount of joining fee requires.