1.Researchers, hoping to determine the percentage of Santa Fe college students who believe in ghosts, went to Santa Fe College to conduct a survey. Random samples of 20 students were taken from each major field of study (ie 20 Mathematics majors, 20 English majors,...)

and were asked whether or not they believed in ghosts. Identify the following:

a.The population

b.The population parameter of interest

c.The sample

d.The sampling method (SRS, stratified, cluster, or systematic)

e. Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest

2.Scientists at a major pharmaceutical firm investigated the effectiveness of 3 herbal compounds (compound A, compound B, and compound C) to treat obesity. 40 volunteers suffering from obesity participated. Subjects were randomly assigned to one of the compounds or to a sugar solution known to have no effect. After 2 months, scientists compared the average difference in weight among the different groups. Identify:

a.The subjects studied

b.The factor(s) in the experiment and the number of levels of each

c.The number of treatments

d.The response variable measured

e.The design (completely randomized, blocked, or matched pairs)

f.Whether it was blinded or not

3.Sample Spaces -list the sample spaces

a.Toss 2 coins one at a time and record the order of heads and tails.

b. Toss a coin and then a die.

c.Toss four coins and record the number of tails.

Round All probabilities to 4 decimal places

4.Draw 1 card from a standard deck of 52.

Let = event that a spade turns up

Red = event that a red card turns up

2 = the event that a 2 turns up

Find the following:

a.P( )

b.P( or Red)

c.P( or 2)

d.P( and Red)

e.Are the events and Red disjoint?

f.P( and 2)

g.Are the events and 2 disjoint?

h.P( | Red)

i.Are the events and Red independent?

j.P( | 2 )

k.Are the events and 2 independent?

5.You roll a fair die three times. What is the probability that you

a.Roll all 3's?

b.You roll all odd numbers?

c.You roll at least one 5?

6.Draw 3 cards from a standard deck of 52 without replacement.

a.P(all hearts)

b.P(no queens)

c.P(at least one heart)

d.P(the 2nd card is the only heart)

7.Real estate ads suggest that 60% of homes for sale have garages, 20% have swimming pools, and 15% have both. What is the probability that a home for sale has

a.A pool or a garage?

b.A pool but no garage?

c.Neither a pool nor a garage?

d.If it is known that a home for sale has a pool, what is the probability that it has a garage?

8.Random Variables

Game-Pick a card from a standard 52 card deck

Cost to play -$3.00

If you choose a Red, you get nothing.

If you choose a , you get $3.00.

If you choose a you get $5.00.

If you choose the Ace of , you get an additional $20.00.

a.Create a probability model for the players resulting amount after 1 play. (just fill out the table)

b. What does the random variable represent? X = ________________

c.Find the player's expected resulting amount after 1 play.

d.Find the standard deviation.

e.Who has the advantage, the player or the person holding the game?

9.Let X and Y be two independent random variables with the following means and

standard deviations.

Mean of X= 80 & Y=65

Standard Deviation of X=65 & Y=8

Find the following.

a.The mean of 3X.

b.The standard deviation of Y+10.

c.The mean of X+Y.

d.The standard deviation of X + Y.

e. The mean of X + 3Y