Consider this random experiment: Experience has shown that 30% of all persons afflicted by a certain illness recover. A drug company has developed a new medication. Ten people with the illness were selected at random and received the medication. Suppose that the medication was absolutely worthless. Let X be the number of patients recovered the illness.

1. What are the possible values of the random variable X?Arrange your answers in ascending order (start from lowest to highest value).
2. Construct and present the probability distribution of X using a probability distribution table:Arrange your X values from lowest to highest. Express your P(X) values in decimal form and round off to two significant figures.
3. Construct and present the probability distribution of X using a probability distribution graph:
4. Find the probability that:Express your answers in decimal form and round off to two significant figures.

4.a. At least eight patients will recover: ( 8) =

4.b. Four or five patients will recover: (=4 5) =

4.c. At most three patients will recover: ( 3) =

5.a. Out of ten people with the illness, compute for the expected number of patients who will recover:

()=

5.b. Briefly interpret the result in A: out of 10people is expected to from the certain illness.

(For the third blank item, input "recover" or "not recover".)

6.a. Compute for the variance of the random variable X.Round off your answer to two decimal places.

6.b. Compute for the standard error of the random variable X.Round off your answer to two decimal places.