Suppose that the average length of stay in a chronic disease hospital of a certain type of patients is 60 days with standard deviation of 15. If it is reasonable to assume that the length of stay follows approximate normal distribution, find the probability that a randomly selected patient from this group will have a length of stay:

greater than 50 days

less than 25 days

between 35 and 80 days

Also, find the probability that a random sample of 25 patients will have an average length of stay

greater than 65 days

less than 56 days

between 58 and 62 days

NB: For each of the questions 2-4, identify the variable, the distribution with justification, the associated parameters and properly write the probabilities notations such as P (4 < X < 9) etc. If steps are not properly shown, you will lose points.