The cost to a patient of a hospital stay depends upon three cost factors and an equation related to the procedure performed. The cost factors are D, H, I (Doctor, Hospital, Insurance) and are independent normal random variables with respective meansD = 0.9134,H = 0.5217,I = 0.3724, and standard deviationsD = 0.1717,H = 0.1101,I = 0.0951. The hospital stay cost formula for procedure L871 is X = 12000D + 9100H 20000I where X is the cost to the patient in dollars, and D, H, and I are the cost factors above.

a) Calculate the expected value of X.

b) Calculate the standard deviation of X.

c) What is the probability that the cost(X) to a patient is more than $10000?

d) What is the probability that the cost to the patient is between $6500 and $10500?

e) If we pick a value k such that the probability that X > k equals .10 then calculate k?

f) What is the probability that the cost to the patient, X, is negative (They pay him)? (This never happened to me.)

g) We look at 6 randomly selected patients subject to procedure L871. What is the probability that all 6 of the selected patients have costs between $6500 and $10500?

h) What is the probability that the hospital cost factor is > .7?

i) What is the probability that D > H for a recently selected patient?

i) Add any comment to the text box below.