There is 20% chance that a customer of one vehicle insurance company will file accident claims within the insurance period. Assume that customers from this insurance company are independent to each other regarding claims.

a) Out of 100 customers from this insurance company, find out the mean and variance of the total number of customers that file accident claims

b) Find the probability that exactly 3 customers will file accident claims within their insurance periods for 20 customers recently insured;

c) Find the probability that at least 2 customers and at most 5 customers will file accident claims within their insurance periods for 20 customers recently insured;

d) Find the probability that at least 2 customers will file accident claims within their insurance periods for 20 customers recently insured;

e) Find the probability that more than 2 customers but less than 5 customers will file accident claims within their insurance periods for 20 customers recently insured;