Choose a woman over 18 years of age at random from the entire U.S. population. Here are the

probabilities for her marital status.

Outcome:

Single Married Widowed Divorced

Probability:

? 0.58 0.12 0.10

3. To make this a legitimate assignment of probabilities, the probability that the woman chosen

is single must be

(a) 1

(b) 0.8

(c) 0.42

(d) 0.02

(e) 0.2

Let the random variable Y = the number of snow days in the Sunnydale school system for one

school year. The probability distribution of Y is given below:

Y

0 1 2 3 4 5 6

P(Y) 0.6 0.2 0.08 ? 0.03 0.02 0.01

The next two questions refer to this random variable.

4. ( ) 3

PY= must be

(a) 0.10

(b) 0.08

(c) 0.02

(d) 0.03

(e) 0.06

5. If there are more than two snow days, extra days will be added to the school year in June.

What is the probability that extra days are added?

(a) 0.12

(b) 0.06

(c) 0.08

(d) 0.20

(e) 0.03

6. It has been estimated that 10% of people in the United States are left-handed. Assume that

figure is accurate. If you select 20 people from this population at random, what is the probability

that at least one is left-handed?

(a) 0.12

(b) 0.27

(c) 0.88

(d) 0.73

(e) 0.39

7. In a recent Gallup poll, 58% of Americans said they agree with the statement, "The benefits

of the space program outweigh the costs." If 10 Americans are chosen at random, what is the

probability that 5 or more agree with this statement?

(a) 0.13

(b) 0.20

(c) 0.22

(d) 0.78

(e) 0.80

Choose an adult woman at random. Let the random variable X = the number of children the

chosen women has had. The next two questions concern these data.

8. The probability that a randomly chosen woman has had 3 or more children is

(a) 0.20

(b) 0.87

(c) 0.13

(d) 0.59

(e) 0.07

9. What is the expected value of the number of children a randomly chosen woman has had?

(a) 0.59

(b) 1.29

(c) 1.0

(d) 2.0

(e) 2.5

10. The probability a person is infected by a certain cold virus is 0.2. In a random sample of 12

people is taken, what is the probability that no more that 5 people will be infected by the cold

virus?

(a) 0.0532

(b) 0.927

(c) 0.9861

(d) 0.9806

(e) 0.0039

11. Which of the following could be quantified as a binomial random variable?

(a) The number of persons in an emergency room

(b) The weights of delivery trucks at a supermarket.

(c) The first time you get a speeding ticket.

(d) The square-foot area of houses being built in Preston Hollow.

(e) The number of free throws a player makes out of 20 shots

It has been estimated that 10% of people in the United States are left-handed. Assume that

figure is accurate. If you select 20 people from this population at random, which of the

following expressions represents the probability that exactly 3 of them are left-handed?

(a)

3 17

20 3

19

10 10

C

(b)

3 17

17 3

19

10 10

C

(c)

17 3

20 3

19

10 10

C

(d)

17 3

17 3

19

10 10

C

(e)

3 20

17 3

19

10 10

C

14. Which of the following is not a condition for the binomial setting?

(a) In any set of n trials, there is at least one success.

(b) There are two possible outcomes for each trial

(c) The trials are independent.

(d) There are a fixed number of trials of a random process.

(e) The probability of success on each trial is the same.

15. Ninety percent of the persons who open a checking account at a particular bank keep the account at

least one year. A random sample of 20 new accounts is taken and interest centers on how many will be

kept open for at least one year. What is the probability that at least 17 of these 20 accounts will be kept

open for at least one year?

(a) 0 (b) .1901 (c) .6561 (d) .6769 (e) .8670

16. Which of the following probability models is valid?

a. Media

TV Radio Magazine Newspaper Other

Probability

0.13 0.18

0.19

0.21 0.29

b. Media

TV Radio Magazine Newspaper Other

Probability

0.18 0.19

0.26

0.27 0.28

c. Media

TV Radio Magazine Newspaper Other

Probability

-0.18 0.36

0.11

0.57 0.14

d. Media

TV Radio Magazine Newspaper Other

Probability

0.13 -0.14

0.15

0.16 0.17

e. Media

TV Radio Magazine Newspaper Other

Probability

0.15 0.17

0.19

0.21 0.27

17. Identify if the following scenarios describe a discrete or continuous random variable.

Explain your choice.

(a) X = The number of persons in an emergency room

(b) W = The weights of delivery trucks at a supermarket.

(c) H = The areas of houses being built in a new subdivision.

18. Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let X =

the number of free throws Faith makes out of 20 shots.

(a) Explain why X is a binomial random variable.

(b) Calculate and interpret the mean of X.

(c) Calculate and interpret the standard deviation of X.

(d) Use the binomial probability formula to find P(X = 19). Interpret this value in context.

(e) Her coach says that he will let the team out of practice early if Faith makes 18 or more free

throws. What is the probability that practice ends early? Show your work.

19. Let Y = the number of siblings for a student at a local high school. Suppose we choose

someone from the school at random. The probability distribution of Y is as follows.

(a) Is Y a discrete or continuous? Explain.

(b) Is this a valid probability distribution? Explain.

(c) Create a histogram for the probability distribution and describe its shape.

(d) Find the probability that the randomly selected student has at least one sibling.

(e) Describe in words what P(Y>2) means and find the probability.