1. Let X equal the number of alpha particles counted by a Geiger counter during 30 seconds. Assume that the distribution of X is Poisson with a mean of 4829. Determine (approximately) P(4776 <= X <= 4857).
2. A die is rolled 24 independent times. Let Y be the sum of the 24 resulting values. Recalling that Y is a random variable of the discrete type approximate: (a) P(Y >= 86) (b) P(Y < 86) (c) P(70 < Y <= 86).
3. The number X of flaws on a certain tape of length one yard follows a Poisson distribution with mean 0.3. We examine n = 100 such tapes and count the total number Y of flaws. Approximate P(Y <= 25).
Please explain each step. Also we have a test coming up and my teacher goes over the material too quickly for us to really understand it and our textbook is the "brief" version so it's useless as well so if you know any sites that explain probability and stats concepts and provide a lot of examples with thorough explantions please list them in your answer as well (don't say Khan Academy I've already tried there and they don't have hardly anything on probability and stats). The test will be covering continous distributions.