In the summer holiday, each student is required to write at least one book report one book report. The following table represents the probability distribution function of the number of book reports (X) a student has written in the summer holiday.

x	1	2	3	4	5
P(X=x)	0.8k	k	0.35	0.15	0.05

(a) What is the value of k?
(b) Find E(X) and σ(X)
(c) Suppose the number of book reports students have written have are independent. In a study group with 8 students, what is the probability that exactly 5 students have written at most 3 book reports?

Answer (a) (b) (c) and show clear calculation steps