Question

1. (4 pts) Fill in the contingency table below using the following information:

800 patients are entered into a trial of a new serum to cure Ebola. The patients are split equally into two groups, one of which is given the serum and one of which is not. Of the group given the serum, eighty percent recover, while only fifty-five percent of those not given the serum recover. Use this information to calculate the numbers to fill in the table. Make sure you get the numbers in the table correct or the rest of your first page won’t be correct!

	Recover	Did Not Recover	Total
Serum
No Serum
Total

2. (2 pts each) Find the probability (in fraction and decimal form) that

1. A randomly selected person recovers.

2. A randomly selected person either received the serum or recovered.

3. A randomly person received the serum and recovered.

4. A randomly-selected person did not recover and got the serum.

5. A person did not recover, given that they received the serum.

3. (11 pts) From the probability distribution given below, find the mean, variance, standard deviation and expected value of the random variable, X. Round your values for variance and standard deviation to two decimal places (if necessary).

X	27	32	54	63	78
P(X)	5/18	1/4	1/12	2/9	1/6

Answer 1

2)

X	P(X)	X*P(X)	X² * P(X)
27	0.2778	7.5	202.500
32	0.2500	8	256.000
54	0.0833	4.5	243.0000
63	0.2222	14	882.0000
78	0.1667	13.0000	1014.0000

mean = E[X] = Σx*P(X) =            47
          
E [ X² ] = ΣX² * P(X) =            2597.5000
          
variance = E[ X² ] - (E[ X ])² =            388.50
          
std dev = √(variance) =            19.71