1. Find the mean of the distribution shown.

x 0 3 5

P(x) 0.36 0.40 0.24

A)  1.88    B)  2.76    C)  1.20    D)  2.40

2. The following distribution is not a probability distribution because

x -5 -4 -3 -2 -1

P(x) 0.11 0.16 0.42 0.16 0.30

A) The probability values are not discrete

B) The probability values do not add to 1

C) The values of x are negative

D) The probability values are not increasing

3. The following distribution is not a probability distribution because

x -5 -4 -3 -2 -1

P(x) 0.20 0.20 –0.23 0.54 0.29

A) A probability is negative C) The probability values are not discrete

B) The probability values do not add to 1 D) A values of x is negative

4. What probability value would be needed to complete the following probability distribution?

x -5 -1 0 1 4

P(x) 0.09 0.25 0.15 0.27

A) 0.24

B) There is no value that would make this a probability distribution

C) 0.12

D) 0.48

5. There are 50,000 people at a stadium watching a soccer match, and 40,000 of them are male. If 3 people are chosen at random, what is the probability that all 3 of them are male?

A) 0.080 C) 0.120

B) 0.020 D) 0.512

6. A researcher surveyed college students to study their opinion about the proposed change in smoking rules. The researcher asked a group of 20 students – 11 of them supported the change, 6 of them did not, and 3 had no opinion. This is not a binomial model because

A)  20 students are not enough for a good sample

B)  The students who strongly supported the change and those who only mildly supported the change are counted the same

C)  There are 3 possible outcomes, not 2

D)  More than half of the students supported the change

7. Which of the following pairs of probability values could complete the following probability distribution?

x -3 -2 -1 0 1 2

P(x) 0.10 0.20 p1 p2 0.12 0.16

A)  p1 = 0.06, p2 = 0.56 

B)  p1 = -.11, p2 = 0.53 

C)  p1 = 0.42, p2 = 0.40 

D)  p1 = 0.02, p2 = 0.40

8. A school is sending 11 children to a camp.  If 20% of the children in the school are first graders, and the 8 children are selected at random, what is the mean and variance of the number of first graders chosen?

A)  The mean is 2.2 and the variance is 1.76 

B)  The mean is 1.6 and the variance is 2.56

C)  The mean is 8 and the variance is 11

D)  The mean is 3 and the variance is 20

9. If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct.  Each question has four possible choices. 

A)  0.17     B)  0.08     C)  0.23     D)  0.19 

10. Find the mean of the distribution shown.

x 1 2

P(x) 0.46 0.54

A)  1.27    B)  1.54    C)  0.81    D)  1.03

11. On a Saturday evening, 34% of the people in Chicago go out to dinner, 18% see a movie, 13% have a party, and 35% stay home. Seventeen people are randomly selected. Can the probability that exactly 4 of them stay home be computed using a binomial model?

A) No, because there are more than two possible outcomes 

B) No, because less than 50% of the people stay home

C) Yes, because the expected number of people who stay home is greater than 4

D) Yes, because this can be restated as a binomial model with 35% of the people staying home and the other 65% not

12. A coin is tossed five times.  Find the probability of getting exactly three heads. 

A)  0.3125     B)  0.3750     C)  0.1563     D)  0.2500 

13. Find the mean of the distribution shown.

x -3 -2 -1 0

P(x) 0.19 0.24 0.40 0.17

A)  1.97    B)  –1.76    C)  –1.45    D)  –1.97

14. What is the standard deviation of the following probability distribution?

x  P(x)   

0 0.20

2 0.05

4 0.35

6 0.25

8 0.15 

A)  3.9     B)  2.6     C)  4.7     D)  5.4 

15. Find the mean of the distribution shown.

x 2 3 4

P(x) 0.30 0.24 0.46

A)  3.16    B)  1.66    C)  2.16    D)  2.66

16. The number of cartoons watched by Mrs. Kelly's first grade class on Saturday morning is shown below.  

x  P(x)    

0 0.15

1 0.20

2 0.30

3 0.10

4 0.20

5 0.05 

What is the mean distribution of the data given above?

A)  1.89     B)  1.18     C)  2.15     D)  1.37 

17. A computer store has 50 printers of which 35 are laser printers and 15 are ink jet printers.  If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers.

A) Mean = 2, Variance = 0.6 C) Mean = 3, Variance = 4

B) Mean = 3, Variance = 2.1 D) Mean = 3, Variance = 0.6

18. A researcher calculated the values and probabilities for a random variable X as shown below. Unfortunately, he erased the last value and needs to figure out what it was. If the mean of X was 2.2, then what was the last value?

x 0 1 3 ?

P(x) .4 .1 .2 .3

A) 9

B) 8

C) 6

D) 5

19. What value would be needed to complete the following probability distribution?

x  P(x)

0 1/3

1 1/8

2 1/8

3

4 1/6 

A)  1/4     B)  1/8     C)  1/12     D)  1/5 

20. The probability of failure for taking the bar exam in Philadelphia is 41%.  If 375 people take the bar exam, what is the expected mean number of failures? 

A)  153.8     B)  90.7     C)  138.1     D)  171.2