In a particular region, the probability that a randomly chosen individual is a smoker is 0.32. A sample of 25 people is chosen from the region, and we define Xi=1 if the ith person is a non-smoker and Xi=0 if the ith person is smoker. What is the distribution of of X1+X2+...+X25. ?

During a particular time of the year, beetles are found in the grass. The number of beetles is thought to follow a Poisson distribution with 3.0 beetles expected per square metre. Suppose that a circular trap is constructed such that the probability of capturing at least one beetle in the trap is 0.9. What is the radius of the trap?