Experience has shown that 20% 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 who recovered from the illness. Part 1. Construct and present the probability distribution of X using a probability distribution table: In the first column, identify the possible values of the random variable . Arrange your values in ascending order (start from the lowest to the highest value). In the second column, compute the probability values, . Express the values in decimal form and round off to two significant figures. X P(X) 0 1 Part 2. Express the probabilities in decimal form and round off to two significant figures. Find the probability that: At least eight patients will recover: P(X ≥ 8)= Four or five patients will recover: P(X = 4 or X = 5)= At most three patients will recover: P(X ≤ 3)=

Experience has shown that 20% 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 who recovered from the illness.

Part 1. Construct and present the probability distribution of X using a probability distribution table:

• In the first column, identify the possible values of the random variable . Arrange your values in ascending order (start from the lowest to the highest value).
• In the second column, compute the probability values, . Express the values in decimal form and round off to two significant figures. 

Part 2. Express the probabilities in decimal form and round off to two significant figures. Find the probability that:

1. At least eight patients will recover: P(X ≥ 8)=
2. Four or five patients will recover: P(X = 4 or X = 5)=
3. At most three patients will recover: P(X ≤ 3)=