I am having trouble with this problem. I can't figure out what type of distribution it has, so I am can't solve it. Can you help?

2. Consider 100 light bulbs that are produced and sold at the same time. For each of the lightbulb, the probability of not working and returned after 80 days of use is 0.15. The company needs to pay $10 for each returned lightbulb. Denote X; as if the ith lightbulb does not work and is returned otherwise, for i = 1, . .. . 100. (a) (2 points) Name the distribution of Xi, and give the name(s) and value(s) of the parameter (s). (b) (3 points) Let Y' be the total number of lightbulbs that will be returned, i.e. Y = Xi+ X2+ ...+ Xion. Name the distribution of Y', and give the name(s) and value(s) of the parameter(s). (c) (4 points) Find the expected value and variance of the total payments Z = 10Y that the company will be responsible for due to returned lightbulbs. Hint: derive the expected value and variance of Y first. (d) (4 points) What is the probability that more than 1 lightbulb are returned? Preserve at least 7 decimal places