4. A national fast food chain provides health insurance to its employees through HMOs (health maintenance organizations) afliated with a national insurance carrier. 0n the basis of the experience of employers similar to this one, the insurance company assumes that an appropri ate model for Y, the number of hospitalizations in any given month is the Poisson distribution with parameter A = 4. (a) Determine the probability that no more than two of the fast food chain's employees are hOSpitalized in the next month. (b) Let X be the number of hospitalizations in a year. What is the distribution of X? What is the mean and standard deviation of X? (c) According to past experience only about 15% of the hospitalizations are due to a serious condition and last more than a week. What is the probability that in a given month there will be at least one employee who will require a lengthy hospitalizations. 5. Y has a PoissOn distributiOn with P(Y 2 1} = %. Find P(Y = 1)