number of accidents is distributed according to a Poisson distribution, and the Highway Safety Division wants us to calculate the probability in any month of exactly 0, 1, 2, 3, or 4 accidents. Solution: Using the Poisson formula, we can calculate the probability of no accidents: = = P(0) = = 0.00674 For exactly one accident: = = P(1) = = 0.03370 For exactly two accidents: = = P(2) = = 0.08425 For exactly three accidents: = = P(3) = = 0.14042 For exactly four accidents: = = P(4) = = 0.17552 Our calculations will answer several questions. If we want to know the probability of 0, 1, or 2 accidents in any month, we can add these probabilities as: P(0,1, or 2) = P(0) + P(1) + P(2) = 0.00674 + 0.03370 + 0.08425 = 0.12469 For, P(3 or fewer) = P(0, 1, 2, or 3) = P(0) + P(1) + P(2) + P(3) = 0.00674 + 0.03370 + 0.08425 + 0.14042 = 0.26511 If we want to calculate the probability of more than three then we must be 0.73489 (1- 0.26511). Important Point: The poisson distribution is a good approximation of the binomial distribution when n is greater than or equal to 20 and p is less than or equal to 0.05. The Normal Distribution It is a continuous probability distribution developed by Karl Gauss. The normal probability distribution is often called Gaussian distribution.
number of accidents is distributed according to a Poisson distribution, and the Highway Safety Division wants us to calculate the probability in any month of exactly 0, 1, 2, 3, or 4 accidents. Solution: Using the Poisson formula, we can calculate the probability of no accidents: P(0) = = = = 0.00674 For exactly one accident: P(1) = = = = 0.03370 For exactly two accidents: P(2) = = = = 0.08425 For exactly three accidents: P(3) = = = = 0.14042 For exactly four accidents: P(4) = = = = 0.17552 Our calculations will answer several questions. If we want to know the probability of 0, 1, or 2 accidents in any month, we can add these probabilities as: P(0,1, or 2) = P(0) + P(1) + P(2) = 0.00674 + 0.03370 + 0.08425 = 0.12469 For, P(3 or fewer) = P(0, 1, 2, or 3) = P(0) + P(1) + P(2) + P(3) = 0.00674 + 0.03370 + 0.08425 + 0.14042 = 0.26511 If we want to calculate the probability of more than three then we must be 0.73489 (1- 0.26511). Important Point: The poisson distribution is a good approximation of the binomial distribution when n is greater than or equal to 20 and p is less than or equal to 0.05. The Normal Distribution It is a continuous probability distribution developed by Karl Gauss. The normal probability distribution is often called Gaussian distribution.
study_material-_quan-_107.docx