Probability based on bivariate normal distribution.
Let X and Y be two related job performance measures for a population of specialized workers. Assume that a model for the joint distribution of these rvs is a bivariate normal distribution with μ1 = 5, μ2 = 10, σ12 = 1, σ22 = 25, and ρ = 4/5. (Here the subscript 1 refers to X and 2 refer to Y.) For a worker whose X score is exactly 5, find the likelihood that her Yscore is between 7 and 19.